Glasnik matematički, Vol. 40 No. 2, 2005.
Izvorni znanstveni članak
An equation on operator algebras and semisimple H*-algebras
Joso Vukman
Sažetak
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.
Ključne riječi
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
Datum izdavanja:
9.11.2005.
Posjeta: 1.005 *