ACTA issues

On automatic surjectivity of Jordan homomorphisms

Lajos Molnár, Borut Zalar

Acta Sci. Math. (Szeged) 61:1-4(1995), 413-424

Abstract. In this paper Jordan *-homomorphisms on rings of bounded operators acting on a Hilbert space and on the ring of bounded infinite sequences are studied. More precisely, we investigate the question whether the Jordan *-homomorphisms, whose ranges contain the finite rank elements, must be surjective or injective. In the first case both questions have affirmative \hbox{answers}. In the second case such homomorphisms are always surjective but not necessarily injective. For the ring of operators it is also proved that *-automorphisms can be characterized among additive mappings using the above range condition and only one one-variable identity.

AMS Subject Classification (1991): 46L40, 46K99, 46L70, 16W10, 54D35

Keyword(s): Jordan *-homomorphism, antihomomorphism, operator algebras, Stone-Čech compactification

Received December 22, 1994. (Registered under 5696/2009.)