The Horn conjecture for compact selfadjoint operators

Details The Horn conjecture for compact selfadjoint operators The Horn conjecture for compact selfadjoint operators

2007-09-07

arxiv.org/abs/0709.1088v1

Mathematics

Functional Analysis

20 pages

Scientific paper

We determine the possible eigenvalues of compact selfadjoint operators A,B,C... with the property that A=B+C+... When all these operators are positive, the eigenvalues were known to be subject to certain inequalities which extend Horn's inequalities from the finite-dimensional case when A=B+C. We find the proper extension of the Horn inequalities and show that they, along with their reverse analogues, provide a complete characterization. Our results also allow us to discuss the more general situation where only some of the eigenvalues of the operators are specified. A special case is the requirement that B+C+... be positive of rank at most r.

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