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Concavity of Eigenvalue Sums and the Spectral Shift Function

✍ Scribed by Vadim Kostrykin

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
170 KB
Volume
176
Category
Article
ISSN
0022-1236

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✦ Synopsis

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 self-adjoint operators on a separable Hilbert space with an arbitrary spectrum. More precisely, we prove that the spectral shift function integrated with respect to the spectral parameter from & to * (from * to + ) is concave (convex) with respect to trace class perturbations. The case of relative trace class perturbations is also considered. 2000

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