Original scientific paper

An equation on operator algebras and semisimple H*-algebras

Joso Vukman

Abstract

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(A3) = AT(A)A

holds for all A A(X). In this case T is of the form T(A) = A for any A A(X) and some F. This result is applied to semisimple H*-algebras.

Keywords

Prime ring; semiprime ring; Banach space; standard operator algebra; H*-algebra; derivation; Jordan derivation; left (right) centralizer; left (right) Jordan centralizer

Hrčak ID:

376

URI

https://hrcak.srce.hr/376

Publication date:

9.11.2005.

Visits: 1.226 *