Characterizing Linear Mappings Through Unital Algebra - Atteya, Mehsin Jabel (Indonesian Journal of Mathematics and Applications, 2025)
In this paper, we characterize the two linear mappings $σ$ and $τ$ satisfying the identity, $x ° y^{\star}=0$ yields $σ(x)° y^{\star}+x° τ(y)^{\star}=0$ for all $x, y \in A$, where $A$ is an $\star$-algebra over a real or complex field $K$ from a unital algebra into its unital $\star$-bimodule. Moreover, we push a complete description of linear mapping that $σ$ is a linear mapping from $A$ into $M$ satisfying $X, Y \in A$, $X ° Y=0$ yields $σ(X)° Y-X° σ(Y)=0$ and each element of $A$ has a weak inverse.