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

Abstract

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

Keywords:

• Hilbert $C^{\ast }$-modules
• inner product orthogonality
• Birkhoff–James orthogonality
• multi-$\mathcal{A}$-linearity
• orthogonality preserving property
• orthogonality equation

2010 Mathematics Subject Classifications:

• 46B20
• 46C50
• 47B49
• 46L05
• 15A69
• 15A86

Acknowledgments

The authors would like to thank the referee for her/his valuable suggestions and comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).