NOTE ON JORDAN TRIPLE (α,β)∗-DERIVATIONS IN H∗-ALGEBRAS

Abstract

The main purpose of this paper is to prove the following result. Let R be a 2-torsion free semiprime *-ring and α, β are endomorphisms of R. Then any Jordan triple (α,β)∗-derivation on R is a Jordan (α,β)∗derivation. As an application of this result, we establish that any linear Jordan triple (α,β)∗-derivation on a semisimple H∗-algebra is a linear Jordan (α,β)∗-derivation.