Orthogonality Hilbert A-modules and operators preserving multi-A-linearity

TL;DR

This paper investigates orthogonality in Hilbert $C^*$-modules, focusing on multi-$ extit{A}$-linearity, orthogonality-preserving operators, and solutions to the orthogonality equation, advancing understanding of structure-preserving maps in this setting.

Contribution

It introduces new results on multi-$ extit{A}$-linearity, orthogonality preservation, and solutions to the orthogonality equation in Hilbert $C^*$-modules, expanding the theoretical framework.

Findings

Characterization of orthogonality in Hilbert $C^*$-modules

New theorems on multi-$ extit{A}$-linearity and its preservation

Solutions to the orthogonality equation in this context

Abstract

In this paper we present results concerning orthogonality in Hilbert $C^*$-modules. Moreover, for a $C^*$-algebra $\mathscr{A}$, we prove theorems concerning the multi-$\mathscr{A}$-linearity and its preservation by $\mathscr{A}$-linear operators. New version of solution of the orthogonality equation on Hilbert $C^*$-modules and mappings preserving orthogonality are also investigated.