An equation on operator algebras and semisimple H*-algebras
Joso Vukman · Glasnik Matematicki · 2005
In this paper we prove the following result: Let X be a Banach space over the real or complex field F and let L(X) be the algebra of all bounded linear operators on X. Suppose there exists an additive mapping T : A(X) → L(X), where A(X) ⊂ L(X) is a standard operator algebra.Suppose that T (A 3 ) = AT (A)A holds for all A ∈ A(X).In this case T is of the form T (A) = λA for any A ∈ A(X) and some λ ∈ F. This result is applied to semisimple H * -algebras.