A generalized Birkhoff-James orthogonality and norm parallelism in unital $C^*$-algebras and their characterizations

TL;DR

This paper introduces a family of generalized norms in unital $C^*$-algebras and explores their implications for Birkhoff-James orthogonality and norm parallelism, providing new characterizations within this algebraic framework.

Contribution

It proposes a new family of generalized norms in $C^*$-algebras and studies their impact on orthogonality and parallelism concepts, offering novel characterizations.

Findings

New generalized norms defined in $C^*$-algebras

Characterizations of orthogonality under these norms

Insights into norm parallelism in algebraic structures

Abstract

We introduced and study a family of generalized norm on $C^*$-algebras and the notion of Birkhoff-James orthogonality and norm-parallelism with respect to these family of generalized norms are investigated.