Isomorphisms and Derivations in Lie C * -Algebras

Abstract

We investigate isomorphisms between $C^{*}$-algebras, Lie $C^{*}$-algebras, and $J{C}^{*}$-algebras, and derivations on $C^{*}$-algebras, Lie $C^{*}$-algebras, and $J{C}^{*}$-algebras associated withthe Cauchy–Jensen functional equation $2f\left(\left(x+y/2\right)+z\right)=f\left(x\right)+f\left(y\right)+2f\left(z\right)$.