Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-10-31T22:55:09.105Z Has data issue: false hasContentIssue false

CLOSED TRIPOTENTS AND WEAK COMPACTNESS IN THE DUAL SPACE OF A JB*-TRIPLE

Published online by Cambridge University Press:  18 August 2006

FRANCISCO J. FERNÁNDEZ-POLO
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spainpacopolo@ugr.es
ANTONIO M. PERALTA
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spainpacopolo@ugr.es
Get access

Abstract

We revise the concept of compact tripotent in the bidual space of a JB*-triple. This concept was introduced by Edwards and Rüttimann generalizing the ideas developed by Akemann for compact projections in the bidual of a C*-algebra. We also obtain some characterizations of weak compactness in the dual space of a JC*-triple, showing that a bounded subset in the dual space of a JC*-triple is relatively weakly compact if and only if its restriction to any abelian maximal subtriple $C$ is relatively weakly compact in the dual of $C$. This generalizes a very useful result by Pfitzner in the setting of C*-algebras. As a consequence we obtain a Dieudonné theorem for JC*-triples which generalizes the one obtained by Brooks, Saitô and Wright for C*-algebras.

Type
Notes and Papers
Copyright
The London Mathematical Society 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)