Abstract:

Let A and B be standard operator algebras on an infinite dimensional Banach space X and ψ: A→B be a preserve unit linear bijection. We prove that if ψ(A。B)=ψ(A)。ψ(B) holds for all A,B∈A with AB=0, then for all A,B∈A either ψ(AB)=ψ(A)ψ(B) or ψ(AB)=ψ(B)ψ(A) holds.

Key words: standard operator algebra; Jordan isomorphism; isomorphism