Invertibility and Fredholm Property of Fock Toeplitz Operators-Reference-Cited by-同舟云学术

Invertibility and Fredholm Property of Fock Toeplitz Operators

Published:2023-07-04 Issue:13 Volume:11 Page:2976
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Xu Chunxu¹^ORCID,Yu Tao²

Affiliation:

1. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

2. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Abstract

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.

Funder

Postdoctoral Foundation of Guangzhou Provence, Guangzhou, Guangdong Province

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/13/2976/pdf

Reference17 articles.

1. Heat flow and Berezin-Toeplitz estimates;Berger;Am. J. Math.,1994

2. Invertibility of Fock Toeplitz operators with positive symbols;Wang;J. Math. Anal. Appl.,2016

3. Invertibility of Toeplitz operators via Berezin transforms;Zhao;J. Oper. Theory,2016

4. On determinants and inverses of some triband Toeplitz matrices with permuted columns;Li;J. Math. Comput. Sci.,2020

5. Compactness characterization of operators in the Toeplitz algebra of the Fock space Fαp;Bauer;J. Funct. Anal.,2012