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arXiv · 0805.4817

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

H. Bercovici·B. Collins·K. Dykema·W. S. Li·D. Timotin
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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.

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H. Bercovici, B. Collins, K. Dykema, W. S. Li, D. Timotin. 2008-05-30. Intersections of Schubert varieties and eigenvalue inequalities in an arbitrary finite factor. https://doi.org/10.1016/j.jfa.2009.09.023

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