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This article is cited in 1 scientific paper (total in 1 paper)
The Ideal of Compact Operators in Real Factors of Types I and II
A. A. Rakhimovab, A. A. Katsc, R. A. Dadakhodjaevd a National University of Uzbekistan named after M. Ulugbek
b Karadeniz Technical University
c St. John's University
d Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan
Abstract:
In the article we study the ideal of relatively compact operators in a real von Neumann factor. We prove a real analog of the Calkin theorem on the uniform closure and uniqueness of the ideal of relatively compact operators. In addition, we show that, unlike complex factors, in a real semifinite factor, up to isomorphism, there exist, in the discrete case, three, and, in the continuous case, two nonzero uniformly closed two-sided real ideals.
Key words:
two-sided ideal, ideal of operators, relatively compact operator, semifinite real factor.
Received: 01.06.2001
Citation:
A. A. Rakhimov, A. A. Kats, R. A. Dadakhodjaev, “The Ideal of Compact Operators in Real Factors of Types I and II”, Mat. Tr., 5:1 (2002), 129–134; Siberian Adv. Math., 13:2 (2003), 90–94
Linking options:
https://www.mathnet.ru/eng/mt104 https://www.mathnet.ru/eng/mt/v5/i1/p129
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Abstract page: | 367 | Full-text PDF : | 128 | References: | 42 | First page: | 1 |
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