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On the definition of real $W^*$-algebras

Authors: J. M. Isidro and A. Rodríguez Palacios
Journal: Proc. Amer. Math. Soc. 124 (1996), 3407-3410
MSC (1991): Primary 46L10, 46L05
MathSciNet review: 1343702
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Abstract: We prove that, if $A$ is a real $C^*$-algebra having a predual $A_*$, then $A_*$ is the unique predual of $A$ and the product of $A$ is $\sigma (A,A_*)$-continuous.

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Additional Information

J. M. Isidro
Affiliation: Facultad de Matemáticas, Universidad de Santiago, 15706 Santiago de Compostela, Spain

A. Rodríguez Palacios
Affiliation: Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Keywords: von Neumann algebras, well framed Banach spaces, uniqueness of preduals, automatic weak* continuity
Received by editor(s): May 8, 1995
Additional Notes: The authors were supported by Acción Integrada Hispano-Alemana HA 94 066 B
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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