Toeplitz operators on large vector-valued Fock spaces

We characterize boundedness and compactness of Toeplitz operators on large vector-valued Fock spaces with Dall'Ara's weights [Adv.\ Math., 285 (2015) 1706--1740] in terms of generalized Berezin transforms, averaging functions, and Carleson measures. To determine Schatten class Toeplitz operators, we introduce the operator-valued Berezin transform and averaging functions.

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Journal
ArXiv.org
Published
2025-04-21
Primary Topic
Holomorphic and Operator Theory
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article
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article

Toeplitz operators on large vector-valued Fock spaces

ArXiv.org
Holomorphic and Operator Theory
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Toeplitz operators on large vector-valued Fock spaces

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Abstract

We characterize boundedness and compactness of Toeplitz operators on large vector-valued Fock spaces with Dall'Ara's weights [Adv.\ Math., 285 (2015) 1706--1740] in terms of generalized Berezin transforms, averaging functions, and Carleson measures. To determine Schatten class Toeplitz operators, we introduce the operator-valued Berezin transform and averaging functions.

ArXiv.org
Openalex Percentile: Top 38%
Holomorphic and Operator Theory
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Toeplitz operators on large vector-valued Fock spaces · ArXiv.org (2025) | TGRS Research Map | TGRS