Glasnik Matematicki, Vol. 40, No.2 (2005), 201-206.

AN EQUATION ON OPERATOR ALGEBRAS AND SEMISIMPLE H*-ALGEBRAS

Joso Vukman

Department of Mathematics, University of Maribor, PEF, Koroška 160, 2000 Maribor, Slovenia
e-mail: joso.vukman@uni-mb.si

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) subset L(X) is a standard operator algebra. Suppose that

T(A3) = AT(A)A

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

2000 Mathematics Subject Classification.   16W10, 46K15, 39B05.

Key words and phrases.   Prime ring, semiprime ring, Banach space, standard operator algebra, H*-algebra, derivation, Jordan derivation, left (right) centralizer, left (right) Jordan centralizer.

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DOI: 10.3336/gm.40.2.02

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