Spectral approximation for Segal-Bargmann space Toeplitz operators

Albrecht Böttcher; Hartmut Wolf

Displaying similar documents to “Spectral approximation for Segal-Bargmann space Toeplitz operators”

Notes on unbounded Toeplitz operators in Segal-Bargmann spaces

D. Cichoń (1996)

Annales Polonici Mathematici

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Relations between different extensions of Toeplitz operators $T_{φ}$ are studied. Additive properties of closed Toeplitz operators are investigated, in particular necessary and sufficient conditions are given and some applications in case of Toeplitz operators with polynomial symbols are indicated.

Toeplitz operators related to certain domains in $C^{n}$

J. Janas (1975)

Studia Mathematica

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Unbounded Toeplitz operators in the Bargmann-Segal space

J. Janas (1991)

Studia Mathematica

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On Pták’s generalization of Hankel operators

Carmen H. Mancera, Pedro José Paúl (2001)

Czechoslovak Mathematical Journal

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In 1997 Pták defined generalized Hankel operators as follows: Given two contractions $T_{1} \in ℬ (ℋ_{1})$ and $T_{2} \in ℬ (ℋ_{2})$ , an operator $X ℋ_{1} \to ℋ_{2}$ is said to be a generalized Hankel operator if $T_{2} X = X T_{1}^{*}$ and $X$ satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations of $T_{1}$ and $T_{2}$ . This approach, call it (P), contrasts with a previous one developed by Pták and Vrbová in 1988, call it (PV), based on the existence of a previously defined generalized Toeplitz operator. There seemed to be a strong...

Schatten class Toeplitz operators acting on large weighted Bergman spaces

Hicham Arroussi, Inyoung Park, Jordi Pau (2015)

Studia Mathematica

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A full description of the membership in the Schatten ideal $S_{p} (A ²_{ω})$ for 0 < p < ∞ of Toeplitz operators acting on large weighted Bergman spaces is obtained.

Asymmetric truncated Toeplitz operators equal to the zero operator

Joanna Jurasik, Bartosz Łanucha (2016)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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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.

Properties of two variables Toeplitz type operators

Elżbieta Król-Klimkowska, Marek Ptak (2016)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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The 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.

Quasinormality and numerical ranges of certain classes of dual Toeplitz operators.

Guediri, Hocine (2010)

Abstract and Applied Analysis

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Toeplitz Quantization for Non-commutating Symbol Spaces such as $S U_{q} (2)$

Stephen Bruce Sontz (2016)

Communications in Mathematics

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Toeplitz quantization is defined in a general setting in which the symbols are the elements of a possibly non-commutative algebra with a conjugation and a possibly degenerate inner product. We show that the quantum group $S U_{q} (2)$ is such an algebra. Unlike many quantization schemes, this Toeplitz quantization does not require a measure. The theory is based on the mathematical structures defined and studied in several recent papers of the author; those papers dealt with some specific examples...

Slant Hankel operators

Subhash Chander Arora, Ruchika Batra, M. P. Singh (2006)

Archivum Mathematicum

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In this paper the notion of slant Hankel operator $K_{ϕ}$ , with symbol $ϕ$ in $L^{\infty}$ , on the space $L^{2} (𝕋)$ , $𝕋$ being the unit circle, is introduced. The matrix of the slant Hankel operator with respect to the usual basis ${z^{i} : i \in ℤ}$ of the space $L^{2}$ is given by $〈 α_{i j} 〉 = 〈 a_{- 2 i - j} 〉$ , where $\sum_{i = - \infty}^{\infty} a_{i} z^{i}$ is the Fourier expansion of $ϕ$ . Some algebraic properties such as the norm, compactness of the operator $K_{ϕ}$ are discussed. Along with the algebraic properties some spectral properties of such operators are discussed. Precisely, it is proved that for...

Generalization of the Newman-Shapiro isometry theorem and Toeplitz operators. II

Dariusz Cichoń (2002)

Studia Mathematica

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The Newman-Shapiro Isometry Theorem is proved in the case of Segal-Bargmann spaces of entire vector-valued functions (i.e. summable with respect to the Gaussian measure on ℂⁿ). The theorem is applied to find the adjoint of an unbounded Toeplitz operator $T_{φ}$ with φ being an operator-valued exponential polynomial.

Local Toeplitz operators based on wavelets: phase space patterns for rough wavelets

Krzysztof Nowak (1996)

Studia Mathematica

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We consider two standard group representations: one acting on functions by translations and dilations, the other by translations and modulations, and we study local Toeplitz operators based on them. Local Toeplitz operators are the averages of projection-valued functions $g \mapsto P_{g, ϕ}$ , where for a fixed function ϕ, $P_{g, ϕ}$ denotes the one-dimensional orthogonal projection on the function $U_{g} ϕ$ , U is a group representation and g is an element of the group. They are defined as integrals $ʃ_{W} P_{g, ϕ} d g$ , where W is an open,...

Truncated Toeplitz Operators on the Polydisk.

Albrecht Böttcher (1990)

Monatshefte für Mathematik

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