$(\alpha,\beta)$-A-Normal Operators in Semi-Hilbertian Spaces

TL;DR

This paper introduces and studies $(eta,eta)$-normal operators within semi-Hilbertian spaces, establishing their properties and inequalities relating their A-operator norm and A-numerical radius.

Contribution

It defines and analyzes $(eta,eta)$-normal operators in semi-Hilbertian spaces, providing new properties and inequalities not previously explored.

Findings

Established properties of $(eta,eta)$-normal operators.

Derived inequalities between A-operator norm and A-numerical radius.

Extended operator theory in semi-Hilbertian space context.

Abstract

In this paper we introduce and prove some properties of $(\alpha;\beta)$-normal operators according to semi-Hilbertian space structures. Furthermore we s,ate various inequalities between the A-operator norm and A-numerical radius of $(\alpha,\beta)$-normal operators in semi Hilbertian spaces.