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.)
|