Hyponormality and quasinormality of unbounded Toeplitz operators with non harmonic symbol on the Fock Sobolev space

TL;DR

This paper investigates the conditions under which unbounded Toeplitz operators with non-harmonic symbols are hyponormal or quasinormal on the Fock-Sobolev space, revealing that quasinormality does not necessarily imply hyponormality.

Contribution

It provides essential criteria for hyponormality and quasinormality of unbounded Toeplitz operators with non-harmonic symbols on the Fock-Sobolev space, highlighting their non-implication relationship.

Findings

Quasinormality does not imply hyponormality for these operators.

Established criteria for hyponormality and quasinormality.

Characterized unbounded Toeplitz operators with non-harmonic symbols.

Abstract

In this paper, we establish the essential criteria for the hyponormality and quasinormality of the unbounded Toeplitz operator $T_{\varphi}$ with non-harmonic symbol, acting on the Fock-Sobolev space $F^{2, m}(\mathbb{C})$. The study shows that quasinormality does not inherently imply hyponormality of unbounded Toeplitz operator with non-harmonic symbols.