Essentially commuting Hankel and Toeplitz operators (original) (raw)

2003, Journal of Functional Analysis

ON HYPONORMALITY AND A COMMUTING PROPERTY OF TOEPLITZ OPERATORS

REVISTA DE LA UNIĀ“ON MATEMĀ“ATICA ARGENTINA, 2024

In this work we give sufficient conditions for hyponormality of Toeplitz operators on a weighted Bergman space when the analytic part of the symbol is a monomial and the conjugate part is a polynomial. We also extend a known commuting property of Toeplitz operators with a harmonic symbol on the Bergman space to weighted Bergman spaces.

On the Commutativity of a Certain Class of Toeplitz Operators

Concrete Operators, 2014

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.

A Sufficient condition for compactness of Hankel operators

arXiv: Complex Variables, 2020

Let Omega\OmegaOmega be a bounded convex domain in mathbbCn\mathbb{C}^{n}mathbbCn. We show that if varphiinC1(overlineOmega)\varphi \in C^{1}(\overline{\Omega})varphiinC1(overlineOmega) is holomorphic along analytic varieties in bOmegab\OmegabOmega, then HqvarphiH^{q}_{\varphi}Hqvarphi, the Hankel operator with symbol varphi\varphivarphi, is compact. We have shown the converse earlier, so that we obtain a characterization of compactness of these operators in terms of the behavior of the symbol relative to analytic structure in the boundary. A corollary is that Toeplitz operators with these symbols are Fredholm (of index zero).

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