*-代数上ξ-*-Jordan-型非线性导子

Nonlinearξ-*-Jordan-Type Derivations on*-Algebras

设A是含单位元I的*-代数且ξ是非零复数.假设A包含非平凡投影P,满足:若XAP=0,则X=0;若XA(I-P)=0,则X=0.如果Φ是A上的非线性ξ-*-Jordan-型导子当且仅当Φ是可加的*-导子,且对所有的A∈A,有Φ(ξA)=ξΦ(A).

Let A be a unital*-algebra with the unit I and letξ∈C{0}.Assume that A contains a nontrivial projection P which satisfies X AP=0 implies X=0 and X A(I-P)=0 implies X=0.ThenΦis a nonlinearξ-*-Jordan-type derivations on A if and only ifΦis an additive*-derivation andΦ(ξA)=ξΦ(A)for all A∈A.