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

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.