Equivalence of projections-Reference-Cited by-同舟云学术

Equivalence of projections

Published:1972 Issue:2 Volume:33 Page:485-490
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Berberian S. K.

Abstract

Theorem: An A W ∗ A{W^\ast } -algebra is the ring generated by its projections if and only if it has no abelian summand. Corollary: Every equivalence in an A W ∗ A{W^\ast } -algebra may be implemented by a partial isometry in the ring generated by the projections of the algebra. The corollary is extended to certain finite Baer ∗ \ast -rings.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1972-033-02/S0002-9939-1972-0295090-6/S0002-9939-1972-0295090-6.pdf

Reference12 articles.

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3. Les anneaux d’opérateurs de classe finie;Dixmier, J.;Ann. Sci. \'{E}cole Norm. Sup. (3),1949

4. Sur la réduction des anneaux d’opérateurs;Dixmier, J.;Ann. Sci. \'{E}cole Norm. Sup. (3),1951

5. \bysame, Les algebres d’opérateurs dans l’espace hilbertien (Algèbres de von Neumann), 2ième éd., Gauthier-Villars, Paris, 1969.

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