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Автор: Grafiati

Опубліковано: 6 вересня 2023

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1

Chō, Muneo. "Spectral properties of p-hyponormal operators." Glasgow Mathematical Journal 36, no. 1 (January 1994): 117–22. http://dx.doi.org/10.1017/s0017089500030627.

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Анотація:

Let ℋ be a complex Hilbert space and B(ℋ) be the algebra of all bounded linear opeators on ℋ. An operator T ∈ B(ℋ) is said to be p-hyponormal if (T*T)p–(TT*)p. If p = 1, T is hyponormal and if p = ½ is semi-hyponormal. It is well known that a p-hyponormal operator is p-hyponormal for q≤p. Hyponormal operators have been studied by many authors. The semi-hyponormal operator was first introduced by D. Xia in [7]. The p-hyponormal operators have been studied by A. Aluthge in [1]. Let T be a p-hyponormal operator and T=U|T| be a polar decomposition of T. If U is unitary, Aluthge in [1] proved the following properties.

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2

Chō, Muneo, Dijana Mosic, Biljana Nacevska-Nastovska, and Taiga Saito. "Spectral properties of square hyponormal operators." Filomat 33, no. 15 (2019): 4845–54. http://dx.doi.org/10.2298/fil1915845c.

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Анотація:

In this paper, we introduce a square hyponormal operator as a bounded linear operator T on a complex Hilbert space H such that T2 is a hyponormal operator, and we investigate some basic properties of this operator. Under the hypothesis ?(T) ? (-?(T)) ? {0}, we study spectral properties of a square hyponormal operator. In particular, we show that if z and w are distinct eigen-values of T and x,y ? H are corresponding eigen-vectors, respectively, then ?x,y? = 0. Also, we define nth hyponormal operators and present some properties of this kind of operators.

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3

Gunawan, Gunawan, and Erni Widiyastuti. "KARAKTERISTIK OPERATOR PARANORMAL- * QUASI." Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika 3, no. 1 (April 30, 2022): 256–73. http://dx.doi.org/10.46306/lb.v3i1.114.

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Анотація:

Given Hilbert space H over the fields of . This study aimed to investigate the paranormal- * quasi operators and their properties in Hilbert space. The study resulted the properties of paranormal- * quasi operators, hyponormal operator, class A operator, Class A- * operator, p- hyponormal operator for p > 0, - paranormal operators, compact operator, and the relationship between them

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4

Journal, Baghdad Science. "Quasi-posinormal operators." Baghdad Science Journal 7, no. 3 (September 5, 2010): 1282–87. http://dx.doi.org/10.21123/bsj.7.3.1282-1287.

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Анотація:

In this paper, we introduce a class of operators on a Hilbert space namely quasi-posinormal operators that contain properly the classes of normal operator, hyponormal operators, M–hyponormal operators, dominant operators and posinormal operators . We study some basic properties of these operators .Also we are looking at the relationship between invertibility operator and quasi-posinormal operator .

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5

Duggal, B. P. "On the spectrum of n-tuples of p-hyponormal operators." Glasgow Mathematical Journal 40, no. 1 (March 1998): 123–31. http://dx.doi.org/10.1017/s0017089500032419.

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Анотація:

Let B(H) denote the algebra of operators (i.e., bounded linear transformations) on the Hilbert space H. A ∈ B (H) is said to be p-hyponormal (0<p<l), if (AA*)γ < (A*A)p. (Of course, a l-hyponormal operator is hyponormal.) The p-hyponormal property is monotonic decreasing in p and a p-hyponormal operator is q-hyponormal operator for all 0<q <p. Let A have the polar decomposition A = U |A|, where U is a partial isometry and |A| denotes the (unique) positive square root of A*A.If A has equal defect and nullity, then the partial isometry U may be taken to be unitary. Let ℋU(p) denote the class of p -hyponormal operators for which U in A = U |A| is unitary. ℋU(l/2) operators were introduced by Xia and ℋU(p) operators for a general 0<p<1 were first considered by Aluthge (see [1,14]); ℋU(p) operators have since been considered by a number of authors (see [3, 4, 5, 9, 10] and the references cited in these papers). Generally speaking, ℋU(p) operators have spectral properties similar to those of hyponormal operators. Indeed, let A ε ℋU(p), (0<p <l/2), have the polar decomposition A = U|A|, and define the ℋW(p + 1/2) operator Â by A = |A|1/2U |A|l/2 Let Â = V |Â| Â= |Â|1/2VÂ|ÂAcirc;|1/2. Then we have the following result.

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6

Han, Young, and Hee Son. "On quasi-M-hyponormal operators." Filomat 25, no. 1 (2011): 37–52. http://dx.doi.org/10.2298/fil1101037h.

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Анотація:

An operator T is called quasi-M -hyponormal if there exists a positive real number M such that T ? (M 2 (T ??)? (T ??))T ? T ? (T ??)(T ??)? T for all ? ? C, which is a generalization of M -hyponormality. In this paper, we consider the local spectral properties for quasi-M -hyponormal operators and Weyl type theorems for algebraically quasi-M-hyponormal operators, respectively. It is also proved that if T is an algebraically quasi-M -hyponormal operator, then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.

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7

Mecheri, Salah. "Positive answer to the invariant and hyperinvariant subspaces problems for hyponormal operators." Georgian Mathematical Journal 29, no. 2 (November 30, 2021): 233–44. http://dx.doi.org/10.1515/gmj-2021-2124.

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Abstract The question whether every operator on infinite-dimensional Hilbert space 𝐻 has a nontrivial invariant subspace or a nontrivial hyperinvariant subspace is one of the most difficult problems in operator theory. This problem is open for more than half a century. A subnormal operator has a nontrivial invariant subspace, but the existence of nontrivial invariant subspace for a hyponormal operator 𝑇 still open. In this paper we give an affirmative answer of the existence of a nontrivial hyperinvariant subspace for a hyponormal operator. More generally, we show that a large classes of operators containing the class of hyponormal operators have nontrivial hyperinvariant subspaces. Finally, every generalized scalar operator on a Banach space 𝑋 has a nontrivial invariant subspace.

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8

Mecheri, S., and T. Prasad. "Fuglede – Putnam type theorems for extension of -hyponormal operators." Ukrains’kyi Matematychnyi Zhurnal 74, no. 1 (January 24, 2022): 89–98. http://dx.doi.org/10.37863/umzh.v74i1.2355.

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Анотація:

UDC 517.9 We consider -quasi--hyponormal operator suchthat for some and prove the Fuglede–Putnam type theorem when adjoint of is -quasi--hyponormal or dominant operators.We also show that two quasisimilar -quasi--hyponormal operators have equal essential spectra.

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9

Duggal, B. P. "A remark on the essential spectra of quasi-similar dominant contractions." Glasgow Mathematical Journal 31, no. 2 (May 1989): 165–68. http://dx.doi.org/10.1017/s0017089500007680.

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Анотація:

We consider operators, i.e. bounded linear transformations, on an infinite dimensional separable complex Hilbert space H into itself. The operator A is said to be dominant if for each complex number λ there exists a number Mλ(≥l) such that ∥(A – λ)*x∥ ≤ Mλ∥A – λ)x∥ for each x∈H. If there exists a number M≥Mλ for all λ, then the dominant operator A is said to be M-hyponormal. The class of dominant (and JW-hyponormal) operators was introduced by J. G. Stampfli during the seventies, and has since been considered in a number of papers, amongst then [7], [11]. It is clear that a 1-hyponormal is hyponormal. The operator A*A is said to be quasi-normal if Acommutes with A*A, and we say that A is subnormal if A has a normal extension. It is known that the classes consisting of these operators satisfy the following strict inclusion relation:

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10

Lauric, Vasile. "Some remarks on the invariant subspace problem for hyponormal operators." International Journal of Mathematics and Mathematical Sciences 28, no. 6 (2001): 359–65. http://dx.doi.org/10.1155/s0161171201011966.

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Анотація:

We make some remarks concerning the invariant subspace problem for hyponormal operators. In particular, we bring together various hypotheses that must hold for a hyponormal operator without nontrivial invariant subspaces, and we discuss the existence of such operators.

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11

Jeon, In Ho. "On joint essential spectra of doubly commuting n-tuples of p-hyponormal operators." Glasgow Mathematical Journal 40, no. 3 (September 1998): 353–58. http://dx.doi.org/10.1017/s0017089500032705.

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AbstractLet A be an operator on a Hillbert space with polar decomposition A = |A|, let Â = |A|½U|A|½ and let Â = V|Â| be the polar decomposition of Â. Write Ã for the operatorÃ = |Â|½V|Â|½. If = (A1,…,AN) is a doubly commuting n-tuple of p-hyponormal operators on a Hillbert space with equal defect and nullity, then = (Ã1,…,Ãn) is a doubly commuting n-tuple of hyponormal operators. In this paper we show thatwhere σ* denotes σTe (Taylor essential spectrum), σTw (Taylor-Weyl spectrum) and σTb (Taylor-Browder spectrum), respectively.

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12

Bekai, Djilali, Abdelkader Benali, and Ali Hakem. "The class of (n,m)power-A-quasi-hyponormal operators in semi-Hilbertian space." Global Journal of Pure and Applied Sciences 27, no. 1 (March 5, 2021): 35–41. http://dx.doi.org/10.4314/gjpas.v27i1.5.

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Анотація:

The concept of K-quasi-hyponormal operators on semi-Hilbertian space is defined by Ould Ahmed Mahmoud Sid Ahmed and Abdelkader Benali in [7]. This paper is devoted to the study of new class of operators on semi-Hilbertian space H, ∥. ∥Acalled (n,m)power-A-quasi-hyponormal denoted [(n,m)QH]A.We give some basic properties of these operators and some examples are also given .An operator T ∈ BA(H) is said to be (n,m) power-A-quasi-hyponormal for some positive operator A and for some positive integers n and m if T⋕((T⋕)mTn— Tn(T⋕)m)T≥A or equivalently AT⋕((T⋕)mTn— Tn(T⋕)m)T≥0

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13

Duggal, B. P. "A generalized commutativity theorem for pk-quasihyponormal operators." Filomat 21, no. 2 (2007): 77–83. http://dx.doi.org/10.2298/fil0702077d.

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Анотація:

For Hilbert space operators A and B, let ?AB denote the generalized derivation ?AB(X) = AX - XB and let /\AB denote the elementary operator rAB(X) = AXB-X. If A is a pk-quasihyponormal operator, A ? pk - QH, and B*is an either p-hyponormal or injective dominant or injective pk - QH operator (resp., B*is an either p-hyponormal or dominant or pk - QH operator), then ?AB(X) = 0 =? SA*B*(X) = 0 (resp., rAB(X) = 0 =? rA*B*(X) = 0). .

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14

Chō, Muneo. "Hyponormal operators on uniformly smooth spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 50, no. 1 (February 1991): 150–59. http://dx.doi.org/10.1017/s1446788700032626.

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Анотація:

AbstractIn this paper we will characterize the spectrum of a hyponormal operator and the joint spectrum of a doubly commuting n-tuple of strongly hyponormal operators on a uniformly smooth space. We also describe some applications of these results.

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15

Bakir, Aissa Nasli, and Salah Mecheri. "Another Version of Fuglede–Putnam Theorem." gmj 16, no. 3 (September 2009): 427–33. http://dx.doi.org/10.1515/gmj.2009.427.

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Abstract In [Yoshino, Proc. Amer. Math. Soc. 95: 571–572, 1985] the author proved that for a 𝑀-hyponormal operator 𝐴* and for a dominant operator 𝐵, 𝐶𝐴 = 𝐵𝐶 implies 𝐶𝐴* = 𝐵*𝐶. In the case where 𝐴* and 𝐵 are normal, this result is known as the Fuglede–Putnam theorem. In this paper, we will extend this result to the case in which 𝐴 is an injective (𝑝, 𝑘)-quasihyponormal operator and 𝐵* is a dominant operator. We also show that the same result remains valid for (𝑝, 𝑘)-quasihyponormal and log-hyponormal operators.

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16

Bayart, Frédéric, and Etienne Matheron. "HYPONORMAL OPERATORS, WEIGHTED SHIFTS AND WEAK FORMS OF SUPERCYCLICITY." Proceedings of the Edinburgh Mathematical Society 49, no. 1 (February 2006): 1–15. http://dx.doi.org/10.1017/s0013091504000975.

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AbstractAn operator $T$ on a Banach space $X$ is said to be weakly supercyclic (respectively $N$-supercyclic) if there exists a one-dimensional (respectively $N$-dimensional) subspace of $X$ whose orbit under $T$ is weakly dense (respectively norm dense) in $X$. We show that a weakly supercyclic hyponormal operator is necessarily a multiple of a unitary operator, and we give an example of a weakly supercyclic unitary operator. On the other hand, we show that hyponormal operators are never $N$-supercyclic. Finally, we characterize $N$-supercyclic weighted shifts.

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17

Mecheri, Salah. "Weyl's Theorem for Algebraically (𝑝, 𝑘)-Quasihyponormal Operators". gmj 13, № 2 (червень 2006): 307–13. http://dx.doi.org/10.1515/gmj.2006.307.

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Анотація:

Abstract Let 𝐴 be a bounded linear operator acting on a Hilbert space 𝐻. The 𝐵-Weyl spectrum of 𝐴 is the set σ 𝐵𝑤(𝐴) of all ⋋ ∈ ℂ such that 𝐴 – ⋋𝐼 is not a 𝐵-Fredholm operator of index 0. Let 𝐸(𝐴) be the set of all isolated eigenvalues of 𝐴. Recently, in [Berkani and Arroud, J. Aust. Math. Soc. 76: 291–302, 2004] the author showed that if 𝐴 is hyponormal, then 𝐴 satisfies the generalized Weyl's theorem σ 𝐵𝑤(𝐴) = σ(𝐴) \ 𝐸(𝐴), and the 𝐵-Weyl spectrum σ 𝐵𝑤(𝐴) of 𝐴 satisfies the spectral mapping theorem. Lee [Han, Proc. Amer. Math. Soc. 128: 2291–2296, 2000] showed that Weyl's theorem holds for algebraically hyponormal operators. In this paper the above results are generalized to an algebraically (𝑝, 𝑘)-quasihyponormal operator which includes an algebraically hyponormal operator.

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18

Lauric, Vasile. "A Note on the Range of the Operator − Defined on." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–6. http://dx.doi.org/10.1155/2009/603041.

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Анотація:

We show how a proof of J. Stampfli can be extended to prove that the operator − defined on the Hilbert-Schmidt class, when is an -hyponormal, -hyponormal, or log-hyponormal operator, has a closed range if and only if is finite.

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19

Khurana, Satish K., and Babu Ram. "M-Cohyponormal powers of composition operators." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 53, no. 1 (August 1992): 9–16. http://dx.doi.org/10.1017/s1446788700035345.

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Анотація:

AbstractLet T1, i = 1, 2 be measurable transformations which define bounded composition operators C Ti on L2 of a σ-finite measure space. Let us denote the Radon-Nikodym derivative of with respect to m by hi, i = 1, 2. The main result of this paper is that if and are both M-hyponormal with h1 ≤ M2(h2 o T2) a.e. and h2 ≤ M2(h1 o T1) a.e., then for all positive integers m, n and p, []* is -hyponormal. As a consequence, we see that if is an M-hyponormal composition operator, then is -hyponormal for all positive integers n.

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20

Diagana, Toka. "Fractional powers of hyponormal operators of Putnam type." International Journal of Mathematics and Mathematical Sciences 2005, no. 12 (2005): 1925–32. http://dx.doi.org/10.1155/ijmms.2005.1925.

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Анотація:

We are concerned with fractional powers of the so-called hyponormal operators of Putnam type. Under some suitable assumptions it is shown that ifA,Bare closed hyponormal linear operators of Putnam type acting on a complex Hilbert spaceℍ, thenD((A+B¯)α)=D(Aα)∩D(Bα)=D((A+B¯)∗α)for eachα∈(0,1). As an application, a large class of the Schrödinger's operator with a complex potentialQ∈Lloc1(ℝd)+L∞(ℝd)is considered.

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21

Emamalipour, H., M. R. Jabbarzadeh, and Sohrabi Chegeni. "Some weak p-hyponormal classes of weighted composition operators." Filomat 31, no. 9 (2017): 2643–56. http://dx.doi.org/10.2298/fil1709643e.

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22

Lauric, Vasile. "Some Estimates of Certain Subnormal and Hyponormal Derivations." International Journal of Mathematics and Mathematical Sciences 2008 (2008): 1–6. http://dx.doi.org/10.1155/2008/362409.

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Анотація:

We prove that if and are subnormal operators and is a bounded linear operator such that is a Hilbert-Schmidt operator, then is also a Hilbert-Schmidt operator and for belongs to a certain class of functions. Furthermore, we investigate the similar problem in the case that , are hyponormal operators and is such that belongs to a norm ideal , and we prove that and for being in a certain class of functions.

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23

Berkani, M., and A. Arroud. "Generalized Weyl's theorem and hyponormal operators." Journal of the Australian Mathematical Society 76, no. 2 (April 2004): 291–302. http://dx.doi.org/10.1017/s144678870000896x.

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AbstractLet T be a bounded linear operator acting on a Hilbert space H. The B-Weyl spectrum of T is the set σBW(T) of all λ ∈ Сsuch that T − λI is not a B-Fredholm operator of index 0. Let E(T) be the set of all isolated eigenvalues of T. The aim of this paper is to show that if T is a hyponormal operator, then T satisfies generalized Weyl's theorem σBW(T) = σ(T)/E(T), and the B-Weyl spectrum σBW(T) of T satisfies the spectral mapping theorem. We also consider commuting finite rank perturbations of operators satisfying generalized Weyl's theorem.

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24

Altwaijry, Najla, Kais Feki, and Nicuşor Minculete. "A New Seminorm for d-Tuples of A-Bounded Operators and Their Applications." Mathematics 11, no. 3 (January 29, 2023): 685. http://dx.doi.org/10.3390/math11030685.

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Анотація:

The aim of this paper was to introduce and investigate a new seminorm of operator tuples on a complex Hilbert space H when an additional semi-inner product structure defined by a positive (semi-definite) operator A on H is considered. We prove the equality between this new seminorm and the well-known A-joint seminorm in the case of A-doubly-commuting tuples of A-hyponormal operators. This study is an extension of a well-known result in [Results Math 75, 93(2020)] and allows us to show that the following equalities rA(T)=ωA(T)=∥T∥A hold for every A-doubly-commuting d-tuple of A-hyponormal operators T=(T1,…,Td). Here, rA(T),∥T∥A, and ωA(T) denote the A-joint spectral radius, the A-joint operator seminorm, and the A-joint numerical radius of T, respectively.

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25

Zuo, Fei, and Junli Shen. "On Subscalarity of Some 2 × 2M-Hyponormal Operator Matrices." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/461567.

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Анотація:

We provide some conditions for2×2operator matrices whose diagonal entries areM-hyponormal operators to be subscalar. As a consequence, we obtain that Weyl type theorem holds for such operator matrices.

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26

Duggal, B. P. "An elementary operator with log-hyponormal, p-hyponormal entries." Linear Algebra and its Applications 428, no. 4 (February 2008): 1109–16. http://dx.doi.org/10.1016/j.laa.2007.09.007.

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27

Duan, YongJiang, and TingTing Qi. "Weakly k-hyponormal and polynomially hyponormal commuting operator pairs." Science China Mathematics 58, no. 2 (October 23, 2014): 405–22. http://dx.doi.org/10.1007/s11425-014-4916-x.

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28

Lauric, Vasile. "Almost -Hyponormal Operators with Weyl Spectrum of Area Zero." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–5. http://dx.doi.org/10.1155/2011/801313.

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29

Chō, Muneo, Masuo Itoh, and Satoru Ōshiro. "Weyl's theorem holds for p-hyponormal operators." Glasgow Mathematical Journal 39, no. 2 (May 1997): 217–20. http://dx.doi.org/10.1017/s0017089500032092.

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Анотація:

Let ℋ be a complex Hilbert space and B(ℋ) the algebra of all bounded linear operators on ℋ. Let ℋ(ℋ) be the algebra of all compact operators of B(ℋ). For an operator T ε B(ℋ), let σ(T), σp(T), σπ(T) and πoo(T) denote the spectrum, the point spectrum, the approximate point spectrum and the set of all isolated eigenvalues of finite multiplicity of T, respectively. We denote the kernel and the range of an operator T by ker(T) and R(T), respectively. For a subset of ℋ, the norm closure of is denoted by . The Weyl spectrum ω(T) of T ε B(ℋ) is defined as the set

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30

Rashid, M. H. M. "On an elementary operator withM-hyponormal operator entries." Mathematische Nachrichten 288, no. 5-6 (December 11, 2014): 670–79. http://dx.doi.org/10.1002/mana.201300095.

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31

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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Анотація:

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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32

Chō, M., S. V. Djordjević, B. P. Duggal, and T. Yamazaki. "On an elementary operator with w-hyponormal operator entries." Linear Algebra and its Applications 433, no. 11-12 (December 2010): 2070–79. http://dx.doi.org/10.1016/j.laa.2010.07.010.

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33

Kubrusly, C. S. "Quasireducible operators." International Journal of Mathematics and Mathematical Sciences 2003, no. 31 (2003): 1993–2002. http://dx.doi.org/10.1155/s0161171203206165.

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Анотація:

We introduce the concept ofquasireducibleoperators. Basic properties and illustrative examples are considered in some detail in order to situate the class of quasireducible operators in its due place. In particular, it is shown thatevery quasinormal operator is quasireducible. The following result links this class with the invariant subspace problem:essentially normal quasireducible operators have a nontrivial invariant subspace, which implies thatquasireducible hyponormal operators have a nontrivial invariant subspace.The paper ends with some open questions on the characterization of the class of all quasireducible operators.

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34

Yu, Dahai. "Hyponormal Toeplitz operators on H2(T) with polynomial symbols." Nagoya Mathematical Journal 144 (December 1996): 179–82. http://dx.doi.org/10.1017/s0027763000006061.

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Анотація:

Let T be the unit circle on the complex plane, H2(T) be the usual Hardy space on T, Tø be the Toeplitz operator with symbol Cowen showed that if f1 and f2 are functions in H such that is in Lø, then Tf is hyponormal if and only if for some constant c and some function g in H∞ with Using it, T. Nakazi and K. Takahashi showed that the symbol of hyponormal Toeplitz operator Tø satisfies and and they described the ø solving the functional equation above. Both of their conditions are hard to check, T. Nakazi and K. Takahashi remarked that even “the question about polynomials is still open” [2]. Kehe Zhu gave a computing process by way of Schur’s functions so that we can determine any given polynomial ø such that Tø is hyponormal [3]. Since no closed-form for the general Schur’s function is known, it is still valuable to find an explicit expression for the condition of a polynomial á such that Tø is hyponormal and depends only on the coefficients of ø, here we have one, it is elementary and relatively easy to check. We begin with the most general case and the following Lemma is essential.

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35

MARY, J. STELLA IRENE, and S. PANAYAPPAN. "SOME PROPERTIES OF CLASS A(k) OPERATORS AND THEIR HYPONORMAL TRANSFORMS." Glasgow Mathematical Journal 49, no. 1 (January 2007): 133–43. http://dx.doi.org/10.1017/s0017089507003497.

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Анотація:

Abstract.In this paper we shall first show that if T is a class A(k) operator then its operator transform $\hat{T}$ is hyponormal. Secondly we prove some spectral properties of T via $\hat{T}$. Finally we show that T has property (β).

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36

Lee, Jae Won, and In Ho Jeon. "RIESZ PROJECTIONS FOR A NON-HYPONORMAL OPERATOR." Korean Journal of Mathematics 24, no. 1 (March 30, 2016): 65–70. http://dx.doi.org/10.11568/kjm.2016.24.1.65.

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37

Yang, Changsen. "Powers of an invertible ω-hyponormal operator". Applied Mathematics-A Journal of Chinese Universities 19, № 3 (вересень 2004): 288–92. http://dx.doi.org/10.1007/s11766-004-0037-6.

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38

Sadraoui, Houcine. "Hyponormality on general Bergman spaces." Filomat 33, no. 17 (2019): 5737–41. http://dx.doi.org/10.2298/fil1917737s.

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Анотація:

A bounded operator T on a Hilbert space is hyponormal if T*T-TT* is positive. We give a necessary condition for the hyponormality of Toeplitz operators on weighted Bergman spaces, for a certain class of radial weights, when the symbol is of the form f+g?, where both functions are analytic and bounded on the unit disk. We give a sufficient condition when f is a monomial.

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39

Changsen, Yang, and Ding Yanfeng. "Application of two operators transform from class a operator to the class of hyponormal operator." Acta Mathematica Scientia 31, no. 1 (January 2011): 93–101. http://dx.doi.org/10.1016/s0252-9602(11)60211-7.

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40

Kittaneh, Fuad. "On zero-trace commutators." Bulletin of the Australian Mathematical Society 34, no. 1 (August 1986): 119–26. http://dx.doi.org/10.1017/s0004972700004561.

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We present some results concerning the trace of certain trace class commutators of operators acting on a separable, complex Hilbert space. It is shown, among other things, that if X is a Hilbert-Schmidt operator and A is an operator such that AX − XA is a trace class operator, then tr (AX − XA) = 0 provided one of the following conditions holds: (a) A is subnormal and A*A − AA* is a trace class operator, (b) A is a hyponormal contraction and 1 − AA* is a trace class operator, (c) A2 is normal and A*A − AA* is a trace class operator, (d) A2 and A3 are normal. It is also shown that if A is a self - adjoint operator, if f is a function that is analytic on some neighbourhood of the closed disc{z: |z| ≥ ||A||}, and if X is a compact operator such that f (A) X − Xf (A) is a trace class operator, then tr (f (A) X − Xf (A))=0.

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41

Campbell, James T., and William E. Hornor. "Localising and seminormal composition operators on L2." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 124, no. 2 (1994): 301–16. http://dx.doi.org/10.1017/s0308210500028481.

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Let (X, ∑, μ) denote a σ-finite measure space. We show that the kernel condition on a weighted composition operator acting on L2(X, ∑, μ), which is necessary for hyponormality of the adjoint, implies that a certain subset of X has the localising property defined by Lambert. For operators satisfying this condition, we find a reducing subspace whose orthocomplement in L2 is annihilated by both the operator and its adjoint, allowing us to obtain characterisations of seminormality for the operator by looking only at the restriction to the reducing subspace. This simplifies the analysis significantly, giving transparent characterisations for the hyponormality and quasinormality of the adjoint, as well as a characterisation of normality for the operator which does not require the computation of any conditional expectations. Several examples are given. We then characterise the semi-hyponormal class for both the operator and its adjoint.

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42

ng Duan, Yongji, Shi ao Pang, and S. yu Wang. "Propagation phenomena for mono-weakly hyponormal operator pairs." Operators and Matrices, no. 1 (2019): 155–68. http://dx.doi.org/10.7153/oam-2019-13-09.

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43

Herrero, Domingo A. "Spectral pictures of hyponormal bilateral operator weighted shifts." Proceedings of the American Mathematical Society 109, no. 3 (March 1, 1990): 753. http://dx.doi.org/10.1090/s0002-9939-1990-1014644-3.

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44

Jabłoński, Zenon Jan, Il Bong Jung, and Jan Stochel. "A non-hyponormal operator generating Stieltjes moment sequences." Journal of Functional Analysis 262, no. 9 (May 2012): 3946–80. http://dx.doi.org/10.1016/j.jfa.2012.02.006.

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45

Chavan, Sameer. "ON OPERATORS CAUCHY DUAL TO 2-HYPEREXPANSIVE OPERATORS." Proceedings of the Edinburgh Mathematical Society 50, no. 3 (October 2007): 637–52. http://dx.doi.org/10.1017/s0013091505001124.

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AbstractThe operator Cauchy dual to a $2$-hyperexpansive operator $T$, given by $T'\equiv T(T^*T)^{-1}$, turns out to be a hyponormal contraction. This simple observation leads to a structure theorem for the $C^*$-algebra generated by a $2$-hyperexpansion, and a version of the Berger–Shaw theorem for $2$-hyperexpansions.As an application of the hyperexpansivity version of the Berger–Shaw theorem, we show that every analytic $2$-hyperexpansive operator with finite-dimensional cokernel is unitarily equivalent to a compact perturbation of a unilateral shift.

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46

McDonald, G., and C. Sundberg. "On the Spectra of Unbounded Subnormal Operators." Canadian Journal of Mathematics 38, no. 5 (October 1, 1986): 1135–48. http://dx.doi.org/10.4153/cjm-1986-057-x.

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Анотація:

Putnam showed in [5] that the spectrum of the real part of a bounded subnormal operator on a Hilbert space is precisely the projection of the spectrum of the operator onto the real line. (In fact he proved this more generally for bounded hyponormal operators.) We will show that this result can be extended to the class of unbounded subnormal operators with bounded real parts.Before proceeding we establish some notation. If T is a (not necessarily bounded) operator on a Hilbert space, then D(T) will denote its domain, and σ(T) its spectrum. For K a subspace of D(T), T|K will denote the restriction of T to K. Norms of bounded operators and elements in Hilbert spaces will be indicated by ‖ ‖. All Hilbert space inner products will be written 〈,〉. If W is a set in C, the closure of W will be written clos W, the topological boundary will be written bdy W, and the projection of W onto the real line will be written π(W),

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47

Hu, Yinyin, Yufeng Lu, and Yixin Yang. "Properties of dual Toeplitz operator on the orthogonal complement of the pluriharmonic Bergman space of the unit ball." Filomat 36, no. 12 (2022): 4265–76. http://dx.doi.org/10.2298/fil2212265h.

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Анотація:

In this paper, we characterize the hyponormal dual Toeplitz operators with special symbols on the orthogonal complement of the pluriharmonic Bergman space of the unit ball. Also we completely characterize the pluriharmonic symbols for (semi)commuting dual Toeplitz operators.

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48

Baghdad, Abderrahim, and Mohamed Chraibi Kaadoud. "On the maximal numerical range of a hyponormal operator." Operators and Matrices, no. 4 (2019): 1163–71. http://dx.doi.org/10.7153/oam-2019-13-77.

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49

Ko, Eun-Gil. "PROPERTIES OF A κTH ROOT OF A HYPONORMAL OPERATOR". Bulletin of the Korean Mathematical Society 40, № 4 (1 листопада 2003): 685–92. http://dx.doi.org/10.4134/bkms.2003.40.4.685.

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50

Haiying, Li. "Powers of an Invertible (s, p)—w—Hyponormal Operator." Acta Mathematica Scientia 28, no. 2 (April 2008): 282–88. http://dx.doi.org/10.1016/s0252-9602(08)60028-4.

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