Toeplitz-type operators on the Fock space $F_{\alpha}^{2}$

Chunxu Xu; Tao Yu

doi:10.4134/BKMS.b220428

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Bull. Korean Math. Soc. 2023; 60(4): 957-969

Online first article May 17, 2023 Printed July 31, 2023

https://doi.org/10.4134/BKMS.b220428

Toeplitz-type operators on the Fock space $F_{\alpha}^{2}$

Chunxu Xu, Tao Yu

Guangzhou University; Dalian University of Technology

Abstract

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Abstract

Let $j$ be a nonnegative integer. We define the Toeplitz-type operators $T_{a}^{(j)}$ with symbol $a\in L^{\infty}(C)$, which are variants of the traditional Toeplitz operators obtained for $j=0$. In this paper, we study the boundedness of these operators and characterize their compactness in terms of its Berezin transform.

Keywords: Toeplitz-type operators, boundedness, compactness, Fock space

MSC numbers: 47B35, 47B10