Commutativity and spectral properties of $k^{th}$-order slant little Hankel operators on the Bergman space

TL;DR

This paper introduces and analyzes the algebraic and spectral properties of $k^{th}$-order slant little Hankel operators on the Bergman space, focusing on their commutativity conditions and spectral characteristics.

Contribution

It defines $k^{th}$-order slant little Hankel operators on the Bergman space and explores their algebraic, spectral, and commutativity properties, which were not previously studied.

Findings

Established algebraic properties of the operators.

Determined spectral characteristics of the operators.

Identified conditions for operator commutativity.

Abstract

In this paper, we introduce the notion of $k^{th}$-order slant little Hankel operator on the Bergman space with essentially bounded harmonic symbols on the unit disc and obtain its algebraic and spectral properties. We have also discussed the conditions under which $k^{th}$-order slant little Hankel operators commute.