Hyponormality of the sum of two Toeplitz operators

TL;DR

This paper investigates the hyponormality and invertibility of combined Toeplitz operators, including cases with linear functional symbols, expanding understanding of their operator properties.

Contribution

It introduces new results on hyponormality and invertibility for sums of Toeplitz operators with complex weights and linear functional symbols.

Findings

Characterized hyponormality conditions for $wT_{\varphi}+T_{\psi}$.

Analyzed invertibility criteria for these operators.

Explored hyponormality when symbols are linear functionals.

Abstract

In this paper, we have studied the hyponormality and invertibility of the operator of type $wT_{\varphi}+T_{\psi}$ where $w$ is any non-zero complex number and $T_{\varphi}, T_{\psi} $ are Toeplitz operators. We have also studied hyponormality when the symbol of Toeplitz operator is a linear functional.