On the Zelmanovian Classification of Prime JB*- and JBW*-Triples

Abstract

This paper is a natural continuation of that of Moreno Galindo and Rodríguez-Palacios (2000). The present paper contains nontrivial reformulations of the previous classification theorem for prime complex JB*-triples, by replacing “matricially decomposed C*-algebras” (a nonfamiliar concept) with “projections in the multiplier algebra of a given C*-algebra.” It also contains as new facts the “converses” of the structure theorems for both complex and real prime JB*-triples. Moreover, the determination of both real and complex JBW*-factors is obtained, and the agreement of the classification of complex JBW*-factors with the general structure theory of JBW*-triples (Horn and Neher, 1988) is proven.

Key Words:

• Prime JB*-triples
• JBW*-factors

AMS Subject Classification (1991):

• 17C65
• 46K70

Acknowledgment

Partially supported by DGICYT Grant PB95-1146 and Junta de Andalucía grant FQM 0199.