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Estimating Eigenvalue Moments via Schatten Norm Bounds on Semigroup Differences

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Abstract

We derive new bounds on the moments of the negative eigenvalues of a selfadjoint operator B. The moments of order \(0<\gamma \leqslant 1\) are estimated in terms of Schatten-norm bounds on the difference of the semigroups generated by B and a reference operator A which is assumed to be nonnegative and selfadjoint. The estimate in the case γ = 1 is sharp.

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  1. Institute of Mathematics, Technical University of Clausthal, 38678, Clausthal-Zellerfeld, Germany

    M. Hansmann

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  1. M. Hansmann
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Correspondence to M. Hansmann.

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Hansmann, M. Estimating Eigenvalue Moments via Schatten Norm Bounds on Semigroup Differences. Math Phys Anal Geom 10, 261–270 (2007). https://doi.org/10.1007/s11040-007-9032-5

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  • DOI: https://doi.org/10.1007/s11040-007-9032-5

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