 99357 Vadim Kostrykin
 Concavity of Eigenvalue Sums and The Spectral Shift Function
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Sep 27, 99

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Abstract. It is well known that the sum of negative (positive) eigenvalues of some finite
Hermitian matrix $V$ is concave (convex) with respect to $V$. Using the theory
of the spectral shift function we generalize this property to selfadjoint
operators on separable Hilbert space with an arbitrary spectrum. More
precisely, we prove that the spectral shift function integrated with respect to
the spectral parameter from $\infty$ to $\lambda$ (from $\lambda$ to
$+\infty$) is concave (convex) with respect to trace class perturbations. The
case of relative trace class perturbations is also considered.
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