Semi-commuting Toeplitz Operators on Fock-Sobolev spaces

TL;DR

This paper characterizes when the semi-commutator of two Toeplitz operators on Fock-Sobolev spaces is zero, revealing differences from previous results in the literature.

Contribution

It provides a new characterization of semi-commuting Toeplitz operators on Fock-Sobolev spaces, differing from earlier known results.

Findings

Semi-commutator of Toeplitz operators is zero under specific conditions.

The result differs from Bauer, Choe, and Koo's earlier findings.

New criteria for semi-commuting Toeplitz operators on Fock-Sobolev spaces.

Abstract

Let $F^{2,m}(\mathbb{C})$ denote the Fock-Sobolev space of complex plane. In this paper, we characterize the semi-commutator of two Toeplitz operators on $F^{2,m}(\mathbb{C})$ is zero. The result is different from the result of Bauer, Choe, and Koo. (J. Funct. Anal., 268 (2015): 3017-3060.)