Set Of The Standard Operator Algebra Subalgebra Lee Triple Homogeneous Additivity And Jordan Operator Algebra The Jordan On The Guide

Let A be a standard operator subalgebra of nest algebra which does not contain the identity operator, acting on a Hilbert space of dimension greater than one. If φ is a bijective Lie triple map from A onto an arbitrary algebra, that is,φ([[a,b],c])一[[φ(a),φ(b)],φ(c)] for all a,b, c∈A, then φ is additive.Let A be a unital Jordan algebra. A linear map d:Aâ†'> 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. In this note, we give the expression of the Jordan derivations of Jordan algebras of all self-adjoint operators and Spin factors, and prove that all local Jordan derivations and2-local Jordan derivations on Spin facors are Jordan derivations.