Compactness characterization of operators in the Toeplitz algebra of the Fock space Fαp

Wolfram Bauer; Joshua Isralowitz

doi:10.1016/j.jfa.2012.04.020

Compactness characterization of operators in the Toeplitz algebra of the Fock space Fαp

Wolfram Bauer
, Joshua Isralowitz

Mathematics and Statistics

University at Albany

University of Göttingen

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

52 Scopus citations

Abstract

For 1<p<∞ let T _p ^α be the norm closure of the algebra generated by Toeplitz operators with bounded symbols acting on the standard weighted Fock space F _α ^p In this paper, we will show that an operator A is compact on Fαp if and only if A∈T _p ^α and the Berezin transform B _α(A) of A vanishes at infinity.

Original language	English
Pages (from-to)	1323-1355
Number of pages	33
Journal	Journal of Functional Analysis
Volume	263
Issue number	5
DOIs	https://doi.org/10.1016/j.jfa.2012.04.020
State	Published - Sep 1 2012

Keywords

Fock spaces
Toeplitz algebra
Toeplitz operators

Access to Document

10.1016/j.jfa.2012.04.020

Cite this

@article{7605d60390f54d96bf56f4f6dcdcd52e,

title = "Compactness characterization of operators in the Toeplitz algebra of the Fock space Fαp",

abstract = "For 1p α be the norm closure of the algebra generated by Toeplitz operators with bounded symbols acting on the standard weighted Fock space F α p In this paper, we will show that an operator A is compact on Fαp if and only if A∈T p α and the Berezin transform B α(A) of A vanishes at infinity.",

keywords = "Fock spaces, Toeplitz algebra, Toeplitz operators",

author = "Wolfram Bauer and Joshua Isralowitz",

year = "2012",

month = sep,

day = "1",

doi = "10.1016/j.jfa.2012.04.020",

language = "English",

volume = "263",

pages = "1323--1355",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "5",

}

TY - JOUR

T1 - Compactness characterization of operators in the Toeplitz algebra of the Fock space Fαp

AU - Bauer, Wolfram

AU - Isralowitz, Joshua

PY - 2012/9/1

Y1 - 2012/9/1

N2 - For 1p α be the norm closure of the algebra generated by Toeplitz operators with bounded symbols acting on the standard weighted Fock space F α p In this paper, we will show that an operator A is compact on Fαp if and only if A∈T p α and the Berezin transform B α(A) of A vanishes at infinity.

AB - For 1p α be the norm closure of the algebra generated by Toeplitz operators with bounded symbols acting on the standard weighted Fock space F α p In this paper, we will show that an operator A is compact on Fαp if and only if A∈T p α and the Berezin transform B α(A) of A vanishes at infinity.

KW - Fock spaces

KW - Toeplitz algebra

KW - Toeplitz operators

UR - https://www.scopus.com/pages/publications/84862987026

U2 - 10.1016/j.jfa.2012.04.020

DO - 10.1016/j.jfa.2012.04.020

M3 - Article

SN - 0022-1236

VL - 263

SP - 1323

EP - 1355

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 5

ER -

Compactness characterization of operators in the Toeplitz algebra of the Fock space Fαp

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this