Additive preserving rank one maps on Hilbert $C^\ast$-modules

TL;DR

This paper characterizes additive maps on Hilbert C*-modules that preserve rank one operators, providing insights into their structure and behavior in the context of operator theory.

Contribution

It introduces a characterization of additive maps that preserve rank one operators on Hilbert C*-modules, a novel contribution to the understanding of operator mappings.

Findings

Identifies conditions under which additive maps preserve rank one operators.

Provides a structural description of such additive maps.

Enhances understanding of operator preservation in Hilbert C*-modules.

Abstract

In this paper, we characterize a class of additive maps on Hilbert $C^\ast$-modules which maps a "rank one" adjointable operators to another rank one operators.