Abstract:

Let A be a unital Jordan algebra. A linear map d: A→A is called a Jordan derivation on A if it satisfies that d(ab)=d(a)。b+a。d(b) for all a,b∈A. Expressions of the Jordan derivations of Jordan algebras of all self-adjoint operators and Spin factors are given. It is proved that all local Jordan derivations and 2-local Jordan derivations on Spin factors are Jordan derivations.

Key words: Jordan algebra; Jordan derivation; Spin factor