Localization and Berezin transform on the Fock space

Jingbo Xia; Dechao Zheng

doi:10.1016/j.jfa.2012.10.003

Localization and Berezin transform on the Fock space

Jingbo Xia
, Dechao Zheng

Mathematics

Chongqing University
Vanderbilt University

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

26 Scopus citations

Abstract

We introduce the notion of sufficiently localized operators on the Fock space. We show that if A is in the C ^*-algebra generated by the class of sufficiently localized operators, then A is compact if and only if its Berezin transform vanishes at infinity. Moreover, we show that this class contains many familiar operators, including all the Toeplitz operators with bounded symbols.

Original language	English
Pages (from-to)	97-117
Number of pages	21
Journal	Journal of Functional Analysis
Volume	264
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2012.10.003
State	Published - Jan 1 2013

Keywords

Berezin transform
Fock space
Localization

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10.1016/j.jfa.2012.10.003

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title = "Localization and Berezin transform on the Fock space",

abstract = "We introduce the notion of sufficiently localized operators on the Fock space. We show that if A is in the C *-algebra generated by the class of sufficiently localized operators, then A is compact if and only if its Berezin transform vanishes at infinity. Moreover, we show that this class contains many familiar operators, including all the Toeplitz operators with bounded symbols.",

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author = "Jingbo Xia and Dechao Zheng",

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T1 - Localization and Berezin transform on the Fock space

AU - Xia, Jingbo

AU - Zheng, Dechao

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N2 - We introduce the notion of sufficiently localized operators on the Fock space. We show that if A is in the C *-algebra generated by the class of sufficiently localized operators, then A is compact if and only if its Berezin transform vanishes at infinity. Moreover, we show that this class contains many familiar operators, including all the Toeplitz operators with bounded symbols.

AB - We introduce the notion of sufficiently localized operators on the Fock space. We show that if A is in the C *-algebra generated by the class of sufficiently localized operators, then A is compact if and only if its Berezin transform vanishes at infinity. Moreover, we show that this class contains many familiar operators, including all the Toeplitz operators with bounded symbols.

KW - Berezin transform

KW - Fock space

KW - Localization

UR - https://www.scopus.com/pages/publications/84869507311

U2 - 10.1016/j.jfa.2012.10.003

DO - 10.1016/j.jfa.2012.10.003

M3 - Article

AN - SCOPUS:84869507311

SN - 0022-1236

VL - 264

SP - 97

EP - 117

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

ER -

Localization and Berezin transform on the Fock space

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Keywords

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