Intersections of Schubert varieties and eigenvalue inequalities in an arbitrary finite factor

Abstract

It is known that the eigenvalues of selfadjoint elements a,b,c with a+b+c=0 in the factor R^omega (ultrapower of the hyperfinite II1 factor) are characterized by a system of inequalities analogous to the classical Horn inequalities of linear algebra. We prove that these inequalities are in fact true for elements of an arbitrary finite factor. A matricial (`complete') form of this result is equivalent to an embedding question formulated by Connes.

41 pages, many figures

References in corpus (2)

• A Linearization of Connes' Embedding Problem
• On a reduction procedure for Horn inequalities in finite von Neumann algebras

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