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

被引：53

作者：

Bauer, Wolfram ^{[1
]}

Isralowitz, Joshua ^{[1
]}

机构：

[1] Univ Gottingen, Inst Math, D-37073 Gottingen, Germany

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 263卷 / 05期

关键词：

Toeplitz algebra; Toeplitz operators; Fock spaces; BEREZIN TRANSFORM; ESSENTIAL NORM;

D O I：

10.1016/j.jfa.2012.04.020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For 1 < p < infinity let T-p(alpha) be the norm closure of the algebra generated by Toeplitz operators with bounded symbols acting on the standard weighted Fock space F-alpha(p). In this paper, we will show that an operator A is compact on F-alpha(p) and only if A is an element of T-p(alpha) and the Berezin transform B-alpha(A) of A vanishes at infinity. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1323 / 1355

页数：33

共 24 条

[1]

[Anonymous], 1991, Banach Spaces for Analysts

[2]

[Anonymous], 1987, Rev. Mat. Iberoamericana

[3]

[Anonymous], 1989, GEN TOPOLOGY CHAPTER

[4]

[Anonymous], 1990, An Introduction to Complex Analysis in Several Variables

[5]

[Anonymous], 2005, GRAD TEXTS MATH

[6] ON A HILBERT SPACE OF ANALYTIC FUNCTIONS AND AN ASSOCIATED INTEGRAL TRANSFORM .1. [J].

BARGMANN, V .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1961, 14 (03) :187-&

[7] Heat flow, BMO, and the compactness of Toeplitz operators [J].

Bauer, W. ;

Coburn, L. A. ;

Isralowitz, J. .

JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 259 (01) :57-78

[8] Berezin-Toeplitz quantization and composition formulas [J].

Bauer, Wolfram .

JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 256 (10) :3107-3142

[9] HEAT-FLOW AND BEREZIN-TOEPLITZ ESTIMATES [J].

BERGER, CA ;

COBURN, LA .

AMERICAN JOURNAL OF MATHEMATICS, 1994, 116 (03) :563-590

[10] TOEPLITZ OPERATORS WITH BMO SYMBOLS ON THE SEGAL-BARGMANN SPACE [J].

Coburn, L. A. ;

Isralowitz, J. ;

Li, Bo .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 363 (06) :3015-3030

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