Invertibility and Fredholm Property of Fock Toeplitz Operators

Chunxu Xu () and Tao Yu
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Chunxu Xu: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
Tao Yu: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Mathematics, 2023, vol. 11, issue 13, 1-9

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 B M O 1 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.

Keywords: Toeplitz operator; Berezin transform; bounded mean oscillation; Fock space; invertible operator; Fredholm operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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