Invertibility and Fredholm Property of Fock Toeplitz Operators

被引：0

作者：

Xu, Chunxu ^{[1
]}

Yu, Tao ^{[2
]}

机构：

[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Peoples R China

[2] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

来源：

MATHEMATICS | 2023年 / 11卷 / 13期

关键词：

Toeplitz operator; Berezin transform; bounded mean oscillation; Fock space; invertible operator; Fredholm operator; SPACES; HANKEL;

D O I：

10.3390/math11132976

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize some necessary and sufficient conditions of invertible Toeplitz operators acting on the Fock space. In particular, we study the Fredholm properties of Toeplitz operators with BMO1 symbols, where their Berezin transforms are bounded functions of vanishing oscillation. We show the Fredholm index of the Toeplitz operator via the winding of its Berezin transform along a sufficiently large circle and provide a characterization of invertible Toeplitz operators with non-negative symbols, possibly unbounded, such that the Berezin transforms of the symbols are bounded and of vanishing oscillation.

引用

页数：9

共 17 条

[1] FREDHOLM THEORY OF TOEPLITZ OPERATORS ON STANDARD WEIGHTED FOCK SPACES [J].

Al-Qabani, Aamena ;

Virtanen, Jani A. .

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2018, 43 :769-783

[2]

Axler S, 1998, INDIANA U MATH J, V47, P387

[3] Mean oscillation and Hankel operators on the Segal-Bargmann space [J].

Bauer, V .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2005, 52 (01) :1-15

[4] Compactness characterization of operators in the Toeplitz algebra of the Fock space Fαp [J].

Bauer, Wolfram ;

Isralowitz, Joshua .

JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 263 (05) :1323-1355

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

BERGER, CA ;

COBURN, LA .

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

[6] TOEPLITZ-OPERATORS ON THE SEGAL-BARGMANN SPACE [J].

BERGER, CA ;

COBURN, LA .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 301 (02) :813-829

[7] 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

[8] Compact Toeplitz operators via the Berezin transform on bounded symmetric domains [J].

Englis, M .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 1999, 33 (04) :426-455

[9] Fredholm Toeplitz operators with VMO symbols and the duality of generalized Fock spaces with small exponents [J].

Hu, Zhangjian ;

Virtanen, Jani A. .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2020, 150 (06) :3163-3186

[10] On determinants and inverses of some triband Toeplitz matrices with permuted columns [J].

Li, Pingyun ;

Jiang, Zhaolin ;

Zheng, Yanpeng .

JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2020, 20 (03) :196-206

← 1 2 →