A generalized notion of orthogonality preserving mappings on inner product modules

Abstract

‎‎‎‎‎In this paper, we define a new concept called ``strongly orthogonality preserving mappings '' for inner product modules, which extends the existing notion of ``orthogonality preserving mappings". Also, we provide a condition that is both necessary and sufficient for a linear map between inner product modules to be strongly orthogonality preserving. Some examples on the definition are given.

Keywords

• strongly orthogonality preserving map‎
• ‎inner product module‎
• ‎$c^*-$algebra‎