# Linear maps behaving like derivations or anti-derivations at orthogonal elements on C*-algebras

## TL;DR

This paper characterizes continuous linear maps on C*-algebras that behave like derivations or anti-derivations at orthogonal elements under various orthogonality conditions, with applications to von Neumann and simple C*-algebras.

## Contribution

It provides a detailed structural characterization of such maps under multiple orthogonality conditions, extending understanding of derivation-like behavior in C*-algebras.

## Key findings

- Characterization of maps acting like derivations at orthogonal elements
- Application of results to von Neumann algebras
- Application to unital simple C*-algebras

## Abstract

Let A be a C*-algebra and d from A into A** be a continuous linear map. We assume that d acts like derivation or anti-derivation at orthogonal elements for several types of orthogonality conditions such as ab=0, ab*=0, ab=ba=0 and ab*=b*a=0. In each case, we characterize the structure of d. Then we apply our results for von Neumann algebras and unital simple C*-algebras.