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Displaying similar documents to “Finite sections of truncated Toeplitz operators”

On the Commutativity of a Certain Class of Toeplitz Operators

Issam Louhichi, Fanilo Randriamahaleo, Lova Zakariasy (2014)

Concrete Operators

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One of the major goals in the theory of Toeplitz operators on the Bergman space over the unit disk D in the complex place C is to completely describe the commutant of a given Toeplitz operator, that is, the set of all Toeplitz operators that commute with it. Here we shall study the commutants of a certain class of quasihomogeneous Toeplitz operators defined on the harmonic Bergman space.

Perturbation of Toeplitz operators and reflexivity

Kamila Kliś-Garlicka (2014)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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It was shown that the space of Toeplitz operators perturbated by finite rank operators is 2-hyperreflexive.

Some eigenvalue estimates for wavelet related Toeplitz operators

Krzysztof Nowak (1993)

Colloquium Mathematicae

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By a straightforward computation we obtain eigenvalue estimates for Toeplitz operators related to the two standard reproducing formulas of the wavelet theory. Our result extends the estimates for Calderón-Toeplitz operators obtained by Rochberg in [R2]. In the first section we recall two standard reproducing formulas of the wavelet theory, we define Toeplitz operators and discuss some of their properties. The second section contains precise statements of our results and their proofs....

Berezin and Berezin-Toeplitz quantizations for general function spaces.

Miroslav Englis (2006)

Revista Matemática Complutense

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The standard Berezin and Berezin-Toeplitz quantizations on a Kähler manifold are based on operator symbols and on Toeplitz operators, respectively, on weighted L-spaces of holomorphic functions (weighted Bergman spaces). In both cases, the construction basically uses only the fact that these spaces have a reproducing kernel. We explore the possibilities of using other function spaces with reproducing kernels instead, such as L-spaces of harmonic functions, Sobolev spaces, Sobolev spaces...

A Reproducing Kernel and Toeplitz Operators in the Quantum Plane

Stephen Bruce Sontz (2013)

Communications in Mathematics

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We define and analyze Toeplitz operators whose symbols are the elements of the complex quantum plane, a non-commutative, infinite dimensional algebra. In particular, the symbols do not come from an algebra of functions. The process of forming operators from non-commuting symbols can be considered as a second quantization. To do this we construct a reproducing kernel associated with the quantum plane. We also discuss the commutation relations of creation and annihilation operators which...