This article is cited in 1 paper

The Ideal of Compact Operators in Real Factors of Types I and II

A. A. Rakhimov^ab, A. A. Kats^c, R. A. Dadakhodjaev<sup>d

a</sup> 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.

UDC: 517.98

Received: 01.06.2001

 English version: Siberian Advances in Mathematics, 2003, 13:2, 90–94

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