The Horn conjecture for sums of compact self-adjoint operators
by
Wing Suet Li
Georgia Tech
Coauthors: H. Bercovici and D. Timotin

We provide a complete characterization of the possible eigenvalues of compact self-adjoint operators A, B⁽¹⁾, B⁽²⁾, ..., B⁽ⁿ⁾ with the property that A=B⁽¹⁾+B⁽²⁾+...+B⁽ⁿ⁾. When all these operators are positive with finite trace, the eigenvalues were known to be subject to certain inequalities which extend Horn's inequalities from the finite dimensional case. Here we find the proper extension of the Horn inequalities to self-adjoint compact operators.

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Date received: February 19, 2008