Mathematical Physics, Analysis and Geometry

, Volume 10, Issue 3, pp 261–270 | Cite as

Estimating Eigenvalue Moments via Schatten Norm Bounds on Semigroup Differences



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.


Eigenvalues Moments Schatten ideals Selfadjoint operators Semigroup difference Spectral shift function 

Mathematics Subject Classifications (2000)

47A10 47A75 81Q10 


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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Institute of MathematicsTechnical University of ClausthalClausthal-ZellerfeldGermany

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