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Academic literature on the topic 'Hyponormal operator'

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Published: 6 September 2023

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Journal articles on the topic "Hyponormal operator"

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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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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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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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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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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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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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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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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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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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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  by A = |A|1/2U |A|l/2 Let  = V |Â| Â= |Â|1/2VÂ|ÂAcirc;|1/2. Then we have the following result.
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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Hyponormal operator"

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Yang, Liming. "Subnormal operators, hyponormal operators, and mean polynomial approximation." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40103.

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We prove quasisimilar subdecomposable operators without eigenvalues have equal essential spectra. Therefore, quasisimilar hyponormal operators have equal essential spectra. We obtain some results on the spectral pictures of cyclic hyponormal operators. An algebra homomorphism π from H∞(G) to L(H) is a unital representation for T if π(1) = I and π(x) = T. It is shown that if the boundary of G has zero area measure, then the unital norm continuous representation for a pure hyponormal operator T is unique and is weak star continuous. It follows that every pure hyponormal contraction is in C.0 Let μ represent a positive, compactly supported Borel measure in the plane, C. For each t in [1, ∞ ), the space Pt(μ) consists of the functions in Lt(μ) that belong to the (norm) closure of the (analytic) polynomials. J. Thomson in [T] has shown that the set of bounded point evaluations, bpe μ, for Pt(μ) is a nonempty simply connected region G. We prove that the measure μ restricted to the boundary of G is absolutely continuous with respect to the harmonic measure on G and the space P2(μ)∩C(spt μ) = A(G), where C(spt μ) denotes the continuous functions on spt μ and A(G) denotes those functions continuous on G ¯ that are analytic on G. We also show that if a function f in P2(μ) is zero a.e. μ in a neighborhood of a point on the boundary, then f has to be the zero function. Using this result, we are able to prove that the essential spectrum of a cyclic, self-dual, subnormal operator is symmetric with respect to the real axis. We obtain a reduction into the structure of a cyclic, irreducible, self-dual, subnormal operator. One may assume, in this inquiry, that the corresponding P2(μ) space has bpe μ = D. Necessary and sufficient conditions for a cyclic, subnormal operator Sμ with bpe μ = D to have a self-dual are obtained under the additional assumption that the measure on the unit circle is log-integrable.
Ph. D.
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2

Pramanick, Paramita. "Trace Estimate For The Determinant Operator And K- Homogeneous Operators." Thesis, 2020. https://etd.iisc.ac.in/handle/2005/4872.

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Let $\boldsymbol T=(T_1, \ldots , T_d)$ be a $d$- tuple of commuting operators on a Hilbert space $\mathcal H$. Assume that $\boldsymbol T$ is hyponormal, that is, $\big [\!\!\big [ \boldsymbol T^*, \boldsymbol T \big ]\!\! \big ]:=\big (\!\!\big ( \big [ T_j^*,T_i] \big )\!\!\big )$ acting on the $d$ - fold direct sum of the Hilbert space $\mathcal H$ is non-negative definite. The commutator $[T_j^*,T_i]$, $1\leq i,j \leq d$, of a finitely ctyclic and hyponormal $d$ - tuple is not necessarily compact and therefore the question of finding trace inequalities for such a $d$- tuple does not arise. A generalization of the Berger-Shaw theorem for a commuting tuple $\boldsymbol T$ of hyponormal operators was obtained by Douglas and Yan decades ago. We discuss several examples of this generalization in an attempt to understand if the crucial hypothesis in their theorem requiring the Krull dimension of the Hilbert module over the polynomial ring defined by the map $p\to p(\boldsymbol T)$, $p\in \mathbb C[\boldsymbol z]$, is optimal or not. Indeed, we find examples $\boldsymbol T$ to show that there is a large class of operators for which $\text{trace}\,[T_j^*,T_i]$, $1\leq j,i \leq d$, is finite but the $d$ - tuple is not finitely polynomially cyclic, which is one of the hypotheses of the Douglas-Yan theorem. We also introduce the weaker notion of ``projectively hyponormal operators" and show that the Douglas-Yan thorem remains valid even under this weaker hypothesis. We introduce the determinant operator $\text{dEt}\,(\big[\!\! \big [\boldsymbol{T}^*, \boldsymbol{T}\big ]\!\! \big ]\big) $, which coincides with the generalized commutator introduced by Helton and Howe earlier. We identify a class $BS_{m, \vartheta}(\Omega)$ consisting of commuting $d$- tuples of hyponormal operators $\boldsymbol T$, $\sigma(\boldsymbol T) = \overbar{\Omega}$, satisfying a growth condition for which the dEt is a non-negative definite operator. We then obtain the trace estimate given in the Theorem below. \begin{thmAbs} Let $\boldsymbol{T}=(T_1,\ldots, T_d)$ be a commuting tuple of operators on a Hilbert space $\mathcal{H}$ such that $\boldsymbol{T}$ is in the class $BS_{m, \vartheta}(\Omega)$. Then the determinant operator $\text{dEt}\,\big(\big[\!\! \big [\boldsymbol{T}^*, \boldsymbol{T}\big ]\!\! \big ]\big)$ is in trace-class and \[\text{trace}\,\big (\text{dEt}\,\big(\big[\!\! \big [\boldsymbol{T}^*, \boldsymbol{T}\big ]\!\!\big]\big)\big )\leq m\, \vartheta \,d!\prod_{i=1}^{d}\|T_i\|^2.\] \end{thmAbs} In the case of a commuting $d$ - tuple $\boldsymbol T$ of operators, where $\sigma(\boldsymbol T)$ is of the form $\overbar{\Omega}_1 \times \cdots \times \overbar{\Omega}_d$, we obtain a slightly different but a related estimate for the trace of $\text{dEt}\,\big(\big[\!\! \big [\boldsymbol{T}^*, \boldsymbol{T}\big ]\!\!\big]\big)\big )$. Explicit computation of $\text{dEt}\,\big(\big[\!\! \big [\boldsymbol{T}^*, \boldsymbol{T}\big ]\!\!\big ]\big)$ in several examples and based on some numerical evidence, we make the following conjecture refining the estimate from the Theorem: \begin{conjAbs} Let $\boldsymbol{T}=(T_1,\ldots, T_d)$ be a commuting tuple of operators on a Hilbert space $\mathcal{H}$ such that $\boldsymbol{T}$ is in the class $BS_{m, \vartheta}(\Omega)$. Then the determinant operator $\text{dEt}\,\big(\big[\!\!\big [\boldsymbol{T}^*, \boldsymbol{T}\big ]\!\! \big ]\big)$ is in trace-class, and \[\text{\rm trace}\,\big (\text{dEt}\,\big(\big[\!\! \big [\boldsymbol{T}^*, \boldsymbol{T}\big ]\!\!\big ]\big) \big )\leq \frac{m d!}{\pi^d} \nu(\overline{\Omega}), \] where $\nu$ is the Lebesgue measure. \end{conjAbs} Let $\Omega$ be an irreducible classical bounded symmetric domain of rank $r$ in $\mathbb C^d.$ Let $\mathbb K$ be the maximal compact subgroup of the identity component $G$ of the biholomorphic automorphism group of the domain $\Omega$. The group $\mathbb K$ consisting of linear transformations acts naturally on any $d$-tuple $\boldsymbol T$ of commuting bounded linear operators by the rule: \[k\cdot\boldsymbol{T}:=\big(k_1(T_1, \ldots, T_d), \ldots, k_d(T_1, \ldots, T_d)\big),\,\,k\in \mathbb K, \] where $k_1(\boldsymbol z), \ldots, k_d(\boldsymbol z)$ are linear polynomials. If the orbit of this action modulo unitary equivalence is a singleton, then we say that $\boldsymbol T$ is $\mathbb{K}$-homogeneous. We realize a certain class of $\mathbb{K}$-homogeneous $d$-tuples $\boldsymbol{T}$ as a $d$ -tuple of multiplication by the coordinate functions $z_1,\ldots ,z_d$ on a reproducing kernel Hilbert space $\mathcal H_K$. (The Hilbert space $\mathcal H_K$ consisting of holomorphic functions defined on $\Omega$ and $K$ is the reproducing kernel.) Using this model we obtain a criterion for (i) boundedness, (ii) membership in the Cowen-Douglas class, (iii) unitary equivalence and similarity of these $d$-tuples. In particular, we show that the adjoint of the $d$-tuple of multiplication by the coordinate functions on the weighted Bergman spaces are in the Cowen-Douglas class $B_1(\Omega)$. For an irreducible bounded symmetric domain $\Omega$ of rank $2$, an explicit description of the operator $\sum_{i=1}^d T_i^*T_i$ is given. Based on this formula, a conjecture giving the form of this operator in any rank $r \geq 1$ was made. This conjecture was recently verified by H. Upmeier.
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To, Meng-Fen, and 杜孟芬. "On hyponormal operators which are similar to their adjoints." Thesis, 1996. http://ndltd.ncl.edu.tw/handle/36665652226053194108.

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Books on the topic "Hyponormal operator"

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1955-, Putinar Mihai, ed. Lectures on hyponormal operators. Basel: Birkhäuser Verlag, 1989.

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Martin, Mircea. Lectures on hyponormal operators. Basel: Birkhäuser Verlag, 1989.

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Martin, Mircea, and Mihai Putinar. Lectures on Hyponormal Operators. Basel: Birkhäuser Basel, 1989. http://dx.doi.org/10.1007/978-3-0348-7466-3.

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Curto, Raúl E. Joint hyponormality of Toeplitz pairs. Providence, RI: American Mathematical Society, 2001.

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Lectures on Hyponormal Operators. Springer My Copy UK, 1989.

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Martin, Mircea, and Mihai Putinar. Lectures on Hyponormal Operators. Birkhauser Verlag, 2012.

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Putinar, Mihai. Lectures on Hyponormal Operators. Springer, 2012.

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Spectral Theory of Hyponormal Operators. Birkhäuser, 2013.

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Xia. Spectral Theory of Hyponormal Operators. Birkhauser Verlag, 2013.

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Curto, Raul E., and Woo Young Lee. Joint Hyponormality of Toeplitz Pairs (Memoirs of the American Mathematical Society). American Mathematical Society, 2001.

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Book chapters on the topic "Hyponormal operator"

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Putinar, Mihai. "Hyponormal Operators and Eigendistributions." In Advances in Invariant Subspaces and Other Results of Operator Theory, 249–73. Basel: Birkhäuser Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-7698-8_20.

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Curto, Raúl E., Paul S. Muhly, and Jingbo Xia. "Hyponormal Pairs of Commuting Operators." In Contributions to Operator Theory and its Applications, 1–22. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-9284-1_1.

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Yakubovich, Dmitry V. "A Note on Hyponormal Operators Associated with Quadrature Domains." In Operator Theory, System Theory and Related Topics, 513–25. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8247-7_23.

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Uchiyama, Mitsuru. "Inequalities for semibounded operators and their applications to log-hyponormal operators." In Recent Advances in Operator Theory and Related Topics, 599–611. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8374-0_33.

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Kubrusly, Carlos S. "Hyponormal Operators." In Hilbert Space Operators, 65–74. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2064-0_7.

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Conway, John. "Hyponormal operators." In Mathematical Surveys and Monographs, 149–62. Providence, Rhode Island: American Mathematical Society, 1991. http://dx.doi.org/10.1090/surv/036/04.

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Curto, Raúl, and Mihai Putinar. "Polynomially Hyponormal Operators." In A Glimpse at Hilbert Space Operators, 195–207. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0347-8_12.

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Putinar, Mihai. "Extreme Hyponormal Operators." In Special Classes of Linear Operators and Other Topics, 249–65. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-9164-6_18.

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Martin, Mircea, and Mihai Putinar. "Operations with Hyponormal Operators." In Lectures on Hyponormal Operators, 115–25. Basel: Birkhäuser Basel, 1989. http://dx.doi.org/10.1007/978-3-0348-7466-3_6.

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Martin, Mircea, and Mihai Putinar. "Subnormal Operators." In Lectures on Hyponormal Operators, 15–40. Basel: Birkhäuser Basel, 1989. http://dx.doi.org/10.1007/978-3-0348-7466-3_2.

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Conference papers on the topic "Hyponormal operator"

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Chō, Muneo, Tadasi Huruya, and Kôtarô Tanahashi. "Unitary dilation for polar decompositions of p-hyponormal operators." In Topological Algebras, their Applications, and Related Topics. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc67-0-11.

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