Compactness and essential norm properties of operators on generalized fock spaces

Joshua Isralowitz

doi:10.7900/jot.2013oct24.2020

Compactness and essential norm properties of operators on generalized fock spaces

Joshua Isralowitz

Mathematics and Statistics

University at Albany

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

The purpose of this paper is to systematically study compactness and essential norm properties of operators on a very general class of weighted Fock spaces over Cⁿ. In particular, we obtain rather strong necessary and sufficient conditions for a wide class of operators (which includes operators in the Toeplitz algebra generated by bounded symbols) to be compact and we obtain related estimates on the essential norm of such operators. Finally, we discuss interesting open problems related to our results.

Original language	English
Pages (from-to)	281-314
Number of pages	34
Journal	Journal of Operator Theory
Volume	73
Issue number	2
DOIs	https://doi.org/10.7900/jot.2013oct24.2020
State	Published - 2015

Keywords

Berezin transform
Compactness
Essential norm
Generalized fock spaces
Toeplitz operators

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abstract = "The purpose of this paper is to systematically study compactness and essential norm properties of operators on a very general class of weighted Fock spaces over Cn. In particular, we obtain rather strong necessary and sufficient conditions for a wide class of operators (which includes operators in the Toeplitz algebra generated by bounded symbols) to be compact and we obtain related estimates on the essential norm of such operators. Finally, we discuss interesting open problems related to our results.",

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AB - The purpose of this paper is to systematically study compactness and essential norm properties of operators on a very general class of weighted Fock spaces over Cn. In particular, we obtain rather strong necessary and sufficient conditions for a wide class of operators (which includes operators in the Toeplitz algebra generated by bounded symbols) to be compact and we obtain related estimates on the essential norm of such operators. Finally, we discuss interesting open problems related to our results.

KW - Berezin transform

KW - Compactness

KW - Essential norm

KW - Generalized fock spaces

KW - Toeplitz operators

UR - https://www.scopus.com/pages/publications/84929233972

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DO - 10.7900/jot.2013oct24.2020

M3 - Article

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VL - 73

SP - 281

EP - 314

JO - Journal of Operator Theory

JF - Journal of Operator Theory

IS - 2

ER -

Compactness and essential norm properties of operators on generalized fock spaces

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Keywords

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