Additivity of Lie Triple Isomorphisms on Standard Operator Subalgebras of Nest Algebras

摘要

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]) = [[Φ(a),Φ(t)],Φ(c)],for all a,b,c ∈A,then Φ is additive.