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This article is cited in 2 scientific papers (total in 2 papers)
Commutative symmetric operator algebras in a Pontrjagin space
A. I. Loginov
Abstract:
In the articles of M. A. Na\v{i}mark a study has been made of commutative symmetric algebras of bounded operators in the space $\mathsf\Pi_k$. A model was constructed within whose framework all these algebras can be realized, and conditions were found for their unitary equivalence. In the present article a study is made of Na\v{i}ark's model, and some alterations are proposed which lead to a number of important simplifications. We single out the classes of so-called singular and regular algebras; the study of an arbitrary algebra reduces to the study of these. A complete description is given of regular algebras that are closed with respect to the operator norm.
Received: 31.05.1968
Citation:
A. I. Loginov, “Commutative symmetric operator algebras in a Pontrjagin space”, Math. USSR-Izv., 3:3 (1969), 515–535
Linking options:
https://www.mathnet.ru/eng/im2158https://doi.org/10.1070/IM1969v003n03ABEH000790 https://www.mathnet.ru/eng/im/v33/i3/p549
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