IMPORTANT NOTICE

The AMS website will be down for maintenance on May 23 between 6:00am - 8:00am EDT. For questions please contact AMS Customer Service at cust-serv@ams.org or (800) 321-4267 (U.S. & Canada), (401) 455-4000 (Worldwide).

 

Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-96-03498-3
MathSciNet review: 1343702
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 1. F. F. Bonsall and J. Duncan, Complete normed algebras, Ergebnisse der Math. und ihrer Grenzgebiete 80, Springer-Verlag, Berlin Heidelberg-New York (1973). MR 54:11013
  • 2. C. H. Chu, T. Dang, B. Russo, and B. Ventura, Surjective isometries of real $C^*$-algebras, J. London Math. Soc. 2 47 (1993), 97--118. MR 94a:46069
  • 3. G. Godefroy, Parties admissibles d'un espace de Banach. Applications, Ann. Sci. Ec. Norm. Sup. 4 série 16 (1983), 109--122. MR 84m:46016
  • 4. K. R. Goodearl, Notes on Real and Complex $C^*$-algebras, Shiva Publ., 1982. MR 85d:46079
  • 5. H. Hanche-Olson and E. Størmer, Jordan operator algebras, Monographs Stud. Math 21 Pitman, Boston-London-Melbourne, 1984. MR 86a:46092
  • 6. J. M. Isidro, W. Kaup, and A. Rodríguez Palacios, On real forms of JB$^*$-triples, Manuscripta Math. 86 (1955), 311--335. MR 96a:46122
  • 7. C. E. Rickart, General theory of Banach algebras, Kreiger, New York (1974). MR 22:5903
  • 8. S. Sakai, $C^*$-algebras and $W^*$-algebras, Berlin-Heidelberg-New York, Springer, 1971. MR 56:1082

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46L10, 46L05

Retrieve articles in all journals with MSC (1991): 46L10, 46L05


Additional Information

J. M. Isidro
Affiliation: Facultad de Matemáticas, Universidad de Santiago, 15706 Santiago de Compostela, Spain
Email: jmisidro@zmat.usc.es

A. Rodríguez Palacios
Affiliation: Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
Email: apalacios@goliat.ugr.es

DOI: https://doi.org/10.1090/S0002-9939-96-03498-3
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

American Mathematical Society