Abstract
Let R be a real AW *-algebra, and suppose that its complexification M = R + iR is also a (complex) AW *-algebra. We prove that R is of type I if and only if so is M.
This is a preview of subscription content, log in via an institution to check access.
References
I. Kaplansky, Ann. Math., 53, 235–249 (1951).
I. Kaplansky, Ann. Math., 56, 460–472 (1952).
I. Kaplansky, Amer. J. Math., 75, 839–858 (1953).
J. Dixmier, Summa Brasil. Math., 2, 151–182 (1951).
S. Albeverio, Sh. A. Ayupov, and A. H. Abduvaitov, On Real AW *-algebras, Preprint No. 37, SFB 611 Bonn, 2002.
B. R. Li, Real Operator Algebras, World Scientific, Singapore-New Jersey-London-Hong Kong, 2002.
S. K. Berberian, Baer *-Rings, Springer-Verlag, Berlin-Heidelberg-New York, 1972.
E. Størmer, Pacific J. Math., 21, 349–370 (1967).
Author information
Authors and Affiliations
Additional information
Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 38, No. 4, pp. 79–81, 2004
Original Russian Text Copyright © by Sh. A. Ayupov
Rights and permissions
About this article
Cite this article
Ayupov, S.A. Real AW *-Algebras of type I. Funct Anal Its Appl 38, 302–304 (2004). https://doi.org/10.1007/s10688-005-0008-6
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10688-005-0008-6