Concavity of Eigenvalue Sums and the Spectral Shift Function

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dc.creatorKostrykin, Vadim
dc.date2001-12-26
dc.date.accessioned2026-07-07T04:45:31Z
dc.date.available2026-07-07T04:45:31Z
dc.descriptionIt 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 $-\infty$ to $λ$ (from $λ$ to $+\infty$) is concave (convex) with respect to trace class perturbations. The case of relative trace class perturbations is also considered.
dc.identifierhttps://arxiv.org/abs/math/0112279
dc.identifierhttp://arxiv.org/abs/math/0112279
dc.identifierJ. Funct. Anal. 176 (2000) 100 - 114
dc.identifierdoi:10.1006/jfan.2000.3620
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62983
dc.subjectSpectral Theory
dc.subjectMathematical Physics
dc.subject47A55, 47A10 (Primary) 47A75, 47A40 (Secondary)
dc.titleConcavity of Eigenvalue Sums and the Spectral Shift Function
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