Characterizing linear mappings through zero products or zero Jordan products

LetAbe a *-algebra andMbe a *-A-bimodule. We study the local properties of *-derivations and *-Jordan derivations from A into M under the following orthogonality conditions on elements inA: ab* = 0, ab*+ b* a = 0 andab* = b*a = 0. We characterize the mappings on zero product determined algebras and zero Jordan product determined algebras. Moreover, we give some applications on C*-algebras, group algebras, matrix algebras, algebras of locally measurable operators and von Neumann algebras.

Automated summary

This article explores the local properties of *-derivations and *-Jordan derivations from A into M under specific orthogonality conditions, and characterizes the mappings on zero product determined algebras and zero Jordan product determined algebras. Furthermore, it provides applications in various algebraic fields.