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Journal articles on the topic 'Toeplitz operator'

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Published: 4 June 2021

Last updated: 31 January 2023

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1

Lee, Jongrak. "Normal Toeplitz Operators on the Fock Spaces." Symmetry 12, no. 10 (September 29, 2020): 1615. http://dx.doi.org/10.3390/sym12101615.

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We characterize normal Toeplitz operator on the Fock spaces F2(C). First, we state basic properties for Toeplitz operator Tφ on F2(C). Next, we study the normal Toeplitz operator Tφ on F2(C) in terms of harmonic symbols φ. Finally, we characterize the normal Toeplitz operators Tφ with non-harmonic symbols acting on F2(C).

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2

Xia, Jin, Xiaofeng Wang, and Guangfu Cao. "Toeplitz Operators on Dirichlet-Type Space of Unit Ball." Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/927513.

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We construct a functionuinL2Bn, dVwhich is unbounded on any neighborhood of each boundary point ofBnsuch that Toeplitz operatorTuis a Schattenp-class0<p<∞operator on Dirichlet-type spaceDBn, dV. Then, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Dirichlet-type spaceDBn, dV. We determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator. We investigate the zero-product problem for several Toeplitz operators with radial symbols. Furthermore, the corresponding commuting problem of Toeplitz operators whose symbols are of the formξkuis studied, wherek ∈ Zn,ξ ∈ ∂Bn, anduis a radial function.

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3

Kim, Sumin, and Jongrak Lee. "Normal Toeplitz Operators on the Bergman Space." Mathematics 8, no. 9 (September 1, 2020): 1463. http://dx.doi.org/10.3390/math8091463.

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In this paper, we give a characterization of normality of Toeplitz operator Tφ on the Bergman space A2(D). First, we state basic properties for Toeplitz operator Tφ on A2(D). Next, we consider the normal Toeplitz operator Tφ on A2(D) in terms of harmonic symbols φ. Finally, we characterize the normal Toeplitz operators Tφ with non-harmonic symbols acting on A2(D).

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4

Guan, Hongyan, Liu Liu, and Yufeng Lu. "Algebraic Properties of Quasihomogeneous and Separately Quasihomogeneous Toeplitz Operators on the Pluriharmonic Bergman Space." Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/252037.

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We study some algebraic properties of Toeplitz operator with quasihomogeneous or separately quasihomogeneous symbol on the pluriharmonic Bergman space of the unit ball inℂn. We determine when the product of two Toeplitz operators with certain separately quasi-homogeneous symbols is a Toeplitz operator. Next, we discuss the zero-product problem for several Toeplitz operators, one of whose symbols is separately quasihomogeneous and the others are quasi-homogeneous functions, and show that the zero-product problem for two Toeplitz operators has only a trivial solution if one of the symbols is separately quasihomogeneous and the other is arbitrary. Finally, we also characterize the commutativity of certain quasihomogeneous or separately quasihomogeneous Toeplitz operators.

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5

Liu, Lanzhe. "Weighted boundedness for Toeplitz type operator associated to general integral operators." Asian-European Journal of Mathematics 07, no. 02 (June 2014): 1450026. http://dx.doi.org/10.1142/s1793557114500260.

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In this paper, we establish the weighted sharp maximal function estimates for the Toeplitz type operators associated to some integral operators and the weighted Lipschitz and BMO functions. As an application, we obtain the boundedness of the Toeplitz type operators on weighted Lebesgue and Morrey spaces. The operator includes Littlewood–Paley operator, Marcinkiewicz operator and Bochner–Riesz operator.

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6

Jurasik, Joanna, and Bartosz Łanucha. "Asymmetric truncated Toeplitz operators equal to the zero operator." Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica 70, no. 2 (December 24, 2016): 51. http://dx.doi.org/10.17951/a.2016.70.2.51.

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Asymmetric truncated Toeplitz operators are compressions of multiplication operators acting between two model spaces. These operators are natural generalizations of truncated Toeplitz operators. In this paper we describe symbols of asymmetric truncated Toeplitz operators equal to the zero operator.

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7

DING, XUANHAO. "THE FINITE SUM OF THE PRODUCTS OF TWO TOEPLITZ OPERATORS." Journal of the Australian Mathematical Society 86, no. 1 (February 2009): 45–60. http://dx.doi.org/10.1017/s1446788708000128.

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AbstractWe consider in this paper the question of when the finite sum of products of two Toeplitz operators is a finite-rank perturbation of a single Toeplitz operator on the Hardy space over the unit disk. A necessary condition is found. As a consequence we obtain a necessary and sufficient condition for the product of three Toeplitz operators to be a finite-rank perturbation of a single Toeplitz operator.

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8

Chen, Dazhao, and Hui Huang. "Sharp function estimates and boundedness for Toeplitz-type operators associated with general fractional integral operators." Open Mathematics 19, no. 1 (January 1, 2021): 1554–66. http://dx.doi.org/10.1515/math-2021-0122.

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Abstract In this paper, we establish some sharp maximal function estimates for certain Toeplitz-type operators associated with some fractional integral operators with general kernel. As an application, we obtain the boundedness of the Toeplitz-type operators on the Lebesgue, Morrey and Triebel-Lizorkin spaces. The operators include the Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.

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9

Pandey, Shesh Kumar, and Gopal Datt. "Multivariate version of slant Toeplitz operators on the Lebesgue space." Asian-European Journal of Mathematics 14, no. 09 (January 20, 2021): 2150152. http://dx.doi.org/10.1142/s1793557121501527.

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The paper introduces the [Formula: see text]th-order slant Toeplitz operator on the Lebesgue space of [Formula: see text]-torus, where [Formula: see text] such that [Formula: see text] for all [Formula: see text]. It investigates certain properties of [Formula: see text]th-order slant Toeplitz operators on the Lebesgue space [Formula: see text]. The paper deals with a system of operator equations, characterizing the [Formula: see text]th-order slant Toeplitz operators. At the end, we discuss certain spectral properties of the considered operator.

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10

Agbor, Dieudonne. "Algebraic Properties of Toeplitz Operators on the Pluri-harmonic Fock Space." Journal of Mathematics Research 9, no. 6 (October 26, 2017): 67. http://dx.doi.org/10.5539/jmr.v9n6p67.

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We study some algebraic properties of Toeplitz operators with radial and quasi homogeneous symbols on the pluriharmonic Fock space over $\mathbb{C}^{n}$. We determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator, the zero-product problem for the product of two Toeplitz operators. Next we characterize the commutativity of Toeplitz operators with quasi homogeneous symbols and finally we study finite rank of the product of Toeplitz operators with quasi homogeneous symbols.

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11

Saito, Kichi-Suke. "Toeplitz operators associated with analytic crossed products." Mathematical Proceedings of the Cambridge Philosophical Society 108, no. 3 (November 1990): 539–49. http://dx.doi.org/10.1017/s0305004100069425.

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The class of Toeplitz operators has attracted the attention of several mathematicians and plays an important part in operator theory and related fields. Here we have a special interest in connection with the theory of shift operators, Toeplitz operators, and Hardy classes of vector and operator valued functions as in [12].

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12

Yang, Jingyu, Liu Liu, and Yufeng Lu. "Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman Space." Journal of Function Spaces and Applications 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/578436.

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We study some algebraic properties of Toeplitz operators with radial or quasihomogeneous symbols on the pluriharmonic Bergman space. We first give the necessary and sufficient conditions for the product of two Toeplitz operators with radial symbols to be a Toeplitz operator and discuss the zero-product problem for several Toeplitz operators with radial symbols. Next, we study the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols. Finally, we also investigate finite rank commutators and semicommutators of two Toeplitz operators with quasihomogeneous symbols.

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13

Lin, HongZhao, and YuFeng Lu. "Toeplitz Operators on the Dirichlet Space of𝔹n." Abstract and Applied Analysis 2012 (2012): 1–21. http://dx.doi.org/10.1155/2012/958201.

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We study the algebraic properties of Toeplitz operators on the Dirichlet space of the unit ball𝔹n. We characterize pluriharmonic symbol for which the corresponding Toeplitz operator is normal or isometric. We also obtain descriptions of conjugate holomorphic symbols of commuting Toeplitz operators. Finally, the commuting problem of Toeplitz operators whose symbols are of the formzpz¯qϕ(|z|2)is studied.

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14

Zhang, Bo, and Yufeng Lu. "Toeplitz Operators with Quasihomogeneous Symbols on the Bergman Space of the Unit Ball." Journal of Function Spaces and Applications 2012 (2012): 1–16. http://dx.doi.org/10.1155/2012/414201.

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We consider when the product of two Toeplitz operators with some quasihomogeneous symbols on the Bergman space of the unit ball equals a Toeplitz operator with quasihomogeneous symbols. We also characterize finite-rank semicommutators or commutators of two Toeplitz operators with quasihomogeneous symbols.

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15

Batra, Ruchika. "ESSENTIALLY λ-RATIONALIZED TOEPLITZ HANKEL OPERATORS." jnanabha 52, no. 02 (2022): 06–22. http://dx.doi.org/10.58250/jnanabha.2022.52202.

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We introduce the notion of Essentially λ-Rationalized Toeplitz Hankel operator on the space L2 for a general complex number λ. Precisely, we define such operators via operator equation λk2 MzK2 X − XMzK1 = K1, where k1 and k2 are non zero integers and K1 is a compact operator on L2. We investigate some properties of the set λ-ERTHO(L2), the set of all Essentially λ-Rationalized Toeplitz Hankel operators of order (k1, k2

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16

Król-Klimkowska, Elżbieta, and Marek Ptak. "Properties of two variables Toeplitz type operators." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 15, no. 1 (December 1, 2016): 97–106. http://dx.doi.org/10.1515/aupcsm-2016-0008.

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AbstractThe investigation of properties of generalized Toeplitz operators with respect to the pairs of doubly commuting contractions (the abstract analogue of classical two variable Toeplitz operators) is proceeded. We especially concentrate on the condition of existence such a non-zero operator. There are also presented conditions of analyticity of such an operator.

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17

Hu, Yinyin, Jia Deng, Tao Yu, Liu Liu, and Yufeng Lu. "Reducing Subspaces of the Dual Truncated Toeplitz Operator." Journal of Function Spaces 2018 (June 3, 2018): 1–9. http://dx.doi.org/10.1155/2018/7058401.

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We define the dual truncated Toeplitz operators and give some basic properties of them. In particular, spectrum and reducing subspaces of some special dual truncated Toeplitz operator are characterized.

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18

MICHALSKA, MAŁGORZATA, and PAWEŁ SOBOLEWSKI. "BOUNDED TOEPLITZ AND HANKEL PRODUCTS ON THE WEIGHTED BERGMAN SPACES OF THE UNIT BALL." Journal of the Australian Mathematical Society 99, no. 2 (June 5, 2015): 237–49. http://dx.doi.org/10.1017/s1446788715000129.

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Let $A_{{\it\alpha}}^{p}$ be the weighted Bergman space of the unit ball in ${\mathcal{C}}^{n}$, $n\geq 2$. Recently, Miao studied products of two Toeplitz operators defined on $A_{{\it\alpha}}^{p}$. He proved a necessary condition and a sufficient condition for boundedness of such products in terms of the Berezin transform. We modify the Berezin transform and improve his sufficient condition for products of Toeplitz operators. We also investigate products of two Hankel operators defined on $A_{{\it\alpha}}^{p}$, and products of the Hankel operator and the Toeplitz operator. In particular, in both cases, we prove sufficient conditions for boundedness of the products.

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19

Nikpour, Mehdi. "On Some Algebraic and Operator-Theoretic Properties of λ-Toeplitz Operators." Journal of Operators 2015 (January 6, 2015): 1–8. http://dx.doi.org/10.1155/2015/172754.

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Based on a spectral problem raised by Barría and Halmos, a new class of Hardy-Hilbert space operators, containing the classical Toeplitz operators, is introduced, and some of their Toeplitz-like algebraic and operator-theoretic properties are studied and explored.

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20

Seddighi, K. "On Quasisimilarity for Toeplitz Operators." Canadian Mathematical Bulletin 28, no. 1 (March 1, 1985): 107–12. http://dx.doi.org/10.4153/cmb-1985-012-4.

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AbstractIn this article we give a sufficient condition for quasisimilar analytic Toeplitz operators to be unitarily equivalent. We also use a result of Deddens and Wong to give a sufficient condition for an operator intertwining two analytic Toeplitz operators to intertwine their inner parts too. Analytic Toeplitz operators with univalent symbols satisfying a suitable normalization that are quasisimilar are shown to have equal symbols.

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21

Böttcher, A., S. Grudsky, and I. Spitkovsky. "Block Toeplitz operators with frequency-modulated semi-almost periodic symbols." International Journal of Mathematics and Mathematical Sciences 2003, no. 34 (2003): 2157–76. http://dx.doi.org/10.1155/s0161171203107107.

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This paper is concerned with the influence of frequency modulation on the semi-Fredholm properties of Toeplitz operators with oscillating matrix symbols. The main results give conditions on an orientation-preserving homeomorphismαof the real line that ensure the following: ifbbelongs to a certain class of oscillating matrix functions (periodic, almost periodic, or semi-almost periodic matrix functions) and the Toeplitz operator generated by the matrix functionb(x)is semi-Fredholm, then the Toeplitz operator with the matrix symbolb(α(x))is also semi-Fredholm.

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22

Cichoń, Dariusz, and Harold S. Shapiro. "Toeplitz operators in Segal-Bargmann spaces of vector-valued functions vector-valued functions." MATHEMATICA SCANDINAVICA 93, no. 2 (December 1, 2003): 275. http://dx.doi.org/10.7146/math.scand.a-14424.

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We discuss new results concerning unbounded Toeplitz operators defined in Segal-Bargmann spaces of (vector-valued) functions, i.e. the space of all entire functions which are square summable with respect to the Gaussian measure in $\mathrm{C}^n$. The problem of finding adjoints of analytic Toeplitz operators is solved in some cases. Closedness of the range of analytic Toeplitz operators is studied. We indicate an example of an entire function inducing a Toeplitz operator, for which the space of polynomials is not a core though it is contained in its domain.

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23

Yang, Jun. "Commuting Quasihomogeneous Toeplitz Operator and Hankel Operator on Weighted Bergman Space." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/408168.

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We characterize the commuting Toeplitz operator and Hankel operator with quasihomogeneous symbols. Also, we use it to show the necessary and sufficient conditions for commuting Toeplitz operator and Hankel operator with ordinary functions.

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24

Farenick, Douglas. "The operator system of Toeplitz matrices." Transactions of the American Mathematical Society, Series B 8, no. 32 (November 17, 2021): 999–1023. http://dx.doi.org/10.1090/btran/83.

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A recent paper of A. Connes and W.D. van Suijlekom [Comm. Math. Phys. 383 (2021), pp. 2021–2067] identifies the operator system of n × n n\times n Toeplitz matrices with the dual of the space of all trigonometric polynomials of degree less than n n . The present paper examines this identification in somewhat more detail by showing explicitly that the Connes–van Suijlekom isomorphism is a unital complete order isomorphism of operator systems. Applications include two special results in matrix analysis: (i) that every positive linear map of the n × n n\times n complex matrices is completely positive when restricted to the operator subsystem of Toeplitz matrices and (ii) that every linear unital isometry of the n × n n\times n Toeplitz matrices into the algebra of all n × n n\times n complex matrices is a unitary similarity transformation. An operator systems approach to Toeplitz matrices yields new insights into the positivity of block Toeplitz matrices, which are viewed herein as elements of tensor product spaces of an arbitrary operator system with the operator system of n × n n\times n complex Toeplitz matrices. In particular, it is shown that min and max positivity are distinct if the blocks themselves are Toeplitz matrices, and that the maximally entangled Toeplitz matrix ξ n \xi _n generates an extremal ray in the cone of all continuous n × n n\times n Toeplitz-matrix valued functions f f on the unit circle S 1 S^1 whose Fourier coefficients f ^ ( k ) \hat f(k) vanish for | k | ≥ n |k|\geq n . Lastly, it is noted that all positive Toeplitz matrices over nuclear C ∗ ^* -algebras are approximately separable.

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25

Ren, Bijun, and Enbin Zhang. "Toeplitz Type Operators Associated with Generalized Calderón-Zygmund Operator on Weighted Morrey Spaces." Journal of Function Spaces 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/8167392.

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LetT1be a generalized Calderón-Zygmund operator or±I(the identity operator), letT2andT4be the linear operators, and letT3=±I. Denote the Toeplitz type operator byTb=T1MbIαT2+T3IαMbT4, whereMbf=bfandIαis the fractional integral operator. In this paper, we investigate the boundedness of the operatorTbon weighted Morrey space whenbbelongs to the weighted BMO spaces.

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26

Lauric, Vasile. "On a weighted Toeplitz operator and its commutant." International Journal of Mathematics and Mathematical Sciences 2005, no. 6 (2005): 823–35. http://dx.doi.org/10.1155/ijmms.2005.823.

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We study the structure of a class of weighted Toeplitz operators and obtain a description of the commutant of each operator in this class. We make some progress towards proving that the only operator in the commutant which is not a scalar multiple of the identity operator and which commutes with a nonzero compact operator is zero. The proof of the main statement relies on a conjecture which is left as an open problem.

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27

Park, Jaehui. "Toeplitz Operators whose Symbols Are Borel Measures." Journal of Function Spaces 2021 (April 7, 2021): 1–11. http://dx.doi.org/10.1155/2021/5599823.

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In this paper, we are concerned with Toeplitz operators whose symbols are complex Borel measures. When a complex Borel measure μ on the unit circle is given, we give a formal definition of a Toeplitz operator T μ with symbol μ , as an unbounded linear operator on the Hardy space. We then study various properties of T μ . Among them, there is a theorem that the domain of T μ is represented by a trichotomy. Also, it was shown that if the domain of T μ contains at least one polynomial, then T μ is densely defined. In addition, we give evidence for the conjecture that T μ with a singular measure μ reduces to a trivial linear operator.

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28

LU, JIN, and XIAOFEN LV. "TOEPLITZ OPERATORS BETWEEN FOCK SPACES." Bulletin of the Australian Mathematical Society 92, no. 2 (June 2, 2015): 316–24. http://dx.doi.org/10.1017/s0004972715000477.

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Given a positive Borel measure ${\it\mu}$ on the $n$-dimensional Euclidean space $\mathbb{C}^{n}$, we characterise the boundedness (and compactness) of Toeplitz operators $T_{{\it\mu}}$ between Fock spaces $F^{\infty }({\it\varphi})$ and $F^{p}({\it\varphi})$ with $0<p\leq \infty$ in terms of $t$-Berezin transforms and averaging functions of ${\it\mu}$. Our result extends recent work of Mengestie [‘On Toeplitz operators between Fock spaces’, Integral Equations Operator Theory78 (2014), 213–224] and others.

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29

DONG, XING-TANG, CONGWEN LIU, and ZE-HUA ZHOU. "QUASIHOMOGENEOUS TOEPLITZ OPERATORS WITH INTEGRABLE SYMBOLS ON THE HARMONIC BERGMAN SPACE." Bulletin of the Australian Mathematical Society 90, no. 3 (June 13, 2014): 494–503. http://dx.doi.org/10.1017/s0004972714000379.

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AbstractIn this paper, we completely determine the commutativity of two Toeplitz operators on the harmonic Bergman space with integrable quasihomogeneous symbols, one of which is of the form $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}e^{ik\theta }r^{\, {m}}$. As an application, the problem of when their product is again a Toeplitz operator is solved. In particular, Toeplitz operators with bounded symbols on the harmonic Bergman space commute with $T_{e^{ik\theta }r^{\, {m}}}$ only in trivial cases, which appears quite different from results on analytic Bergman space in Čučković and Rao [‘Mellin transform, monomial symbols, and commuting Toeplitz operators’, J. Funct. Anal.154 (1998), 195–214].

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30

GUENTNER, ERIK, and NIGEL HIGSON. "A NOTE ON TOEPLITZ OPERATORS." International Journal of Mathematics 07, no. 04 (August 1996): 501–13. http://dx.doi.org/10.1142/s0129167x9600027x.

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We study Toeplitz operators on Bergman spaces using techniques from the analysis of Dirac-type operators on complete Riemannian manifolds, and prove an index theorem of Boutet de Monvel from this point of view. Our approach is similar to that of Baum and Douglas [2], but we replace boundary value theory for the Dolbeaut operator with much simpler estimates on complete manifolds.

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31

PARK, EFTON. "THE INDEX OF TOEPLITZ OPERATORS ON FREE TRANSFORMATION GROUP C*-ALGEBRAS." Bulletin of the London Mathematical Society 34, no. 1 (January 2002): 84–90. http://dx.doi.org/10.1112/s0024609301008554.

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Let Γ be a discrete group acting on a compact manifold X, let V be a Γ-equivalent Hermitian vector bundle over X, and let D be a first-order elliptic self-adjoint Γ-equivalent differential operator acting on sections of V. This data is used to define Toeplitz operators with symbols in the transformation group C*-algebra C(X)[rtimes ]Γ, and it is shown that if the symbol of such a Toeplitz operator is invertible, then the operator is Fredholm. In the case where Γ is finite and acts freely on X, a geometric-topological formula for the index is stated that involves an explicitly constructed differential form associated to the symbol.

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32

García, Alma, and Nikolai Vasilevski. "Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball." Journal of Function Spaces 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/306168.

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We extend the known results on commutative Banach algebras generated by Toeplitz operators with radial quasi-homogeneous symbols on the two-dimensional unit ball. Spherical coordinates previously used hid a possibility to detect an essentially wider class of symbols that can generate commutative Banach Toeplitz operator algebras. We characterize these new algebras describing their properties and, under a certain extra condition, construct the corresponding Gelfand theory.

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33

Schlichenmaier, Martin. "Berezin-Toeplitz Quantization for Compact Kähler Manifolds. A Review of Results." Advances in Mathematical Physics 2010 (2010): 1–38. http://dx.doi.org/10.1155/2010/927280.

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This article is a review on Berezin-Toeplitz operator and Berezin-Toeplitz deformation quantization for compact quantizable Kähler manifolds. The basic objects, concepts, and results are given. This concerns the correct semiclassical limit behaviour of the operator quantization, the unique Berezin-Toeplitz deformation quantization (star product), covariant and contravariant Berezin symbols, and Berezin transform. Other related objects and constructions are also discussed.

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34

Gupta, Anuradha, and Aastha Malhotra. "Complex symmetry and normality of Toeplitz composition operators on the hardy space." Filomat 36, no. 7 (2022): 2281–91. http://dx.doi.org/10.2298/fil2207281g.

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In this paper, we investigate the conditions under which the Toeplitz composition operator on the Hardy space H2 becomes complex symmetric with respect to a certain conjugation. We also study various normality conditions for the Toeplitz composition operator on H2.

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35

Câmara, M. Cristina. "Toeplitz operators and Wiener-Hopf factorisation: an introduction." Concrete Operators 4, no. 1 (November 27, 2017): 130–45. http://dx.doi.org/10.1515/conop-2017-0010.

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Abstract Wiener-Hopf factorisation plays an important role in the theory of Toeplitz operators. We consider here Toeplitz operators in the Hardy spaces Hp of the upper half-plane and we review how their Fredholm properties can be studied in terms of a Wiener-Hopf factorisation of their symbols, obtaining necessary and sufficient conditions for the operator to be Fredholm or invertible, as well as formulae for their inverses or one-sided inverses when these exist. The results are applied to a class of singular integral equations in L−1(ℝ)

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36

Ma, Pan, Fugang Yan, Dechao Zheng, and Kehe Zhu. "Mixed products of Toeplitz and Hankel operators on the Fock space." Journal of Operator Theory 84, no. 1 (May 15, 2020): 35–47. http://dx.doi.org/10.7900/jot.2018dec10.2246.

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For entire functions f and g we determine exactly when the product H¯¯¯fT¯¯¯g of the Hankel operator H¯¯¯f and the Toeplitz operator T¯¯¯g is bounded on the Fock space F2α. This solves a natural companion to Sarason's Toeplitz product problem.

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37

Bolourchian, Elahe, and Bijan Ahmadi Kakavandi. "An approximate approach to the structured distance to normality of Toeplitz operators." Quarterly of Applied Mathematics 79, no. 3 (March 25, 2021): 431–43. http://dx.doi.org/10.1090/qam/1589.

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A classical theorem from Brown and Halmos asserts that a Toeplitz operator T ( f ) T(f) is normal if and only if the range of its generator f : T → C f:\mathbb {T}\rightarrow \mathbb {C} is included in a straight line. In this paper, discretizing f ( T ) f(\mathbb {T}) and using the Principal Component Analysis method to project it onto a ‘best’ line segment in L 2 L^2 -norm, we propose a numerical method to find the nearest normal Toeplitz operator from T ( f ) T(f) in the norm | | | T ( f ) | | | ≔ ‖ f ‖ L 2 ( T ) {\left \vert \kern -0.25ex\left \vert \kern -0.25ex\left \vert T(f)\right \vert \kern -0.25ex\right \vert \kern -0.25ex\right \vert }\coloneq \Vert f \Vert _{L^2(\mathbb {T})} which is weaker than the operator norm. Besides, we introduce an index for the distance from normality of Toeplitz operators which is invariant under the transformations f ↦ a f + b f\mapsto a f+b for all a ∈ R a\in \mathbb {R} and b ∈ C b \in \mathbb {C} with a ≠ 0 a\neq 0 .

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38

Takahashi, Katsutoshi. "On Quasisimilarity for Analytic Toeplitz Operators." Canadian Mathematical Bulletin 31, no. 1 (March 1, 1988): 111–16. http://dx.doi.org/10.4153/cmb-1988-017-7.

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AbstractLet f be a function in H∞. We show that if f is inner or if the commutant of the analytic Toeplitz operator Tf is equal to that of Tb for some finite Blaschke product b, then any analytic Toeplitz operator quasisimilar to Tf is unitarily equivalent to Tf.

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39

Barrenechea, A. L. "Shift commutator algebras and multipliers." Filomat 32, no. 17 (2018): 5837–43. http://dx.doi.org/10.2298/fil1817837b.

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We determine the precise structure of all multipliers on the commutator algebra associated to the shift operator on a Hilbert space. The problem has its own interest by its connection with the theory of Toeplitz and Laurent operators.

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40

Fricain, Emmanuel, Andreas Hartmann, and William T. Ross. "Range Spaces of Co-Analytic Toeplitz Operators." Canadian Journal of Mathematics 70, no. 6 (November 20, 2018): 1261–83. http://dx.doi.org/10.4153/cjm-2017-057-4.

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AbstractIn this paper we discuss the range of a co-analytic Toeplitz operator. These range spaces are closely related to de Branges–Rovnyak spaces (in some cases they are equal as sets). In order to understand its structure, we explore when the range space decomposes into the range of an associated analytic Toeplitz operator and an identifiable orthogonal complement. For certain cases, we compute this orthogonal complement in terms of the kernel of a certain Toeplitz operator on the Hardy space, where we focus on when this kernel is a model space (backward shift invariant subspace). In the spirit of Ahern–Clark, we also discuss the non-tangential boundary behavior in these range spaces. These results give us further insight into the description of the range of a co-analytic Toeplitz operator as well as its orthogonal decomposition. Our Ahern–Clark type results, which are stated in a general abstract setting, will also have applications to related sub-Hardy Hilbert spaces of analytic functions such as the de Branges–Rovnyak spaces and the harmonically weighted Dirichlet spaces.

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41

Choi, Ki Seong. "TOEPLITZ TYPE OPERATOR IN ℂn." Journal of the Chungcheong Mathematical Society 27, no. 4 (November 15, 2014): 697–705. http://dx.doi.org/10.14403/jcms.2014.27.4.697.

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42

Sun, Zhi Ling, and Yu Feng Lu. "Toeplitz Operators on the Weighted Pluriharmonic Bergman Space with Radial Symbols." Abstract and Applied Analysis 2011 (2011): 1–15. http://dx.doi.org/10.1155/2011/210596.

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We construct an operatorRwhose restriction onto weighted pluriharmonic Bergman Spacebμ2(Bn)is an isometric isomorphism betweenbμ2(Bn)andl2#. Furthermore, using the operatorRwe prove that each Toeplitz operatorTawith radial symbols is unitary to the multication operatorγa,μI. Meanwhile, the Wick function of a Toeplitz operator with radial symbol gives complete information about the operator, providing its spectral decomposition.

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43

Harutyunyan, Anahit, and Wolfgang Lusky. "Toeplitz operators on weighted spaces of holomorphic functions." MATHEMATICA SCANDINAVICA 103, no. 1 (September 1, 2008): 40. http://dx.doi.org/10.7146/math.scand.a-15067.

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We define a notion of Toeplitz operator on certain spaces of holomorphic functions on the unit disk and on the complex plane which are endowed with a weighted sup-norm. We establish boundedness and compactness conditions, give norm estimates and characterize the essential spectrum of these operators for many symbols.

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44

Arora, S. C., and Ritu Kathuria. "On th-Order Slant Weighted Toeplitz Operator." Scientific World Journal 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/960853.

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Let be a sequence of positive numbers with , when and when . A th-order slant weighted Toeplitz operator on is given by , where is the multiplication on and is an operator on given by , being the orthonormal basis for . In this paper, we define a th-order slant weighted Toeplitz matrix and characterise in terms of this matrix. We further prove some properties of using this characterisation.

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45

Sadraoui, Houcine, Borhen Halouani, Mubariz T. Garayev, and Adel AlShehri. "Hyponormality on a Weighted Bergman Space." Journal of Function Spaces 2020 (August 5, 2020): 1–7. http://dx.doi.org/10.1155/2020/8398012.

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A bounded Hilbert space operator T is hyponormal if T∗T−TT∗ is a positive operator. We consider the hyponormality of Toeplitz operators on a weighted Bergman space. We find a necessary condition for hyponormality in the case of a symbol of the form f+g¯ where f and g are bounded analytic functions on the unit disk. We then find sufficient conditions when f is a monomial.

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46

Arora, S. C., and Jyoti Bhola. "Essentiallyλ-Hankel Operators." Journal of Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/865396.

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The notion of essentiallyλ-Hankel operators is introduced on the spaceH2. In addition to the discussion of some algebraic and topological properties of the setessHankλ, the set of all essentiallyλ-Hankel operators onH2, it is shown that an essentially Toeplitz Rhaly operator with determining sequence〈an〉is inessHankλλ≠0if and only iflimn→∞n+1an=0.

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47

梁, 金金. "Algebraic Properties of H-Toeplitz Operator." Advances in Applied Mathematics 10, no. 12 (2021): 4489–97. http://dx.doi.org/10.12677/aam.2021.1012478.

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48

Liu, Lanzhe. "Weighted boundedness for toeplitz type operators associated to singular integral operator with non-smooth kernel." Filomat 30, no. 9 (2016): 2489–502. http://dx.doi.org/10.2298/fil1609489l.

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In this paper, the weighted boundedness of the Toeplitz type operator associated to some singular integral operator with non-smooth kernel on Lebesgue spaces are obtained. To do this, some weighted sharp maximal function inequalities for the operator are proved.

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49

Datt, Gopal, and Bhawna Bansal Gupta. "Essential commutativity and spectral properties of slant Hankel operators over Lebesgue spaces." Journal of Mathematical Physics 63, no. 6 (June 1, 2022): 061703. http://dx.doi.org/10.1063/5.0086628.

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In this paper, the commutative and spectral properties of a kth-order slant Hankel operator ( k ≥ 2, a fixed integer) on the Lebesgue space of n-dimensional torus, [Formula: see text], where [Formula: see text] is the unit circle, are studied. Characterizations for the commutativity and essential commutativity between higher order slant Hankel operators and slant Toeplitz operators have been obtained. The presence of an open disk in the point spectrum of a kth-order slant Hankel operator with a unimodular inducing function has also been ensured.

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50

Cload, Bruce. "Toeplitz operators in the commutant of a composition operator." Studia Mathematica 133, no. 2 (1999): 187–96. http://dx.doi.org/10.4064/sm-133-2-187-196.

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