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On Schatten–von Neumann Classes and Trace Class Estimates

  • Fritz Gesztesy
  • Marcus Waurick
Chapter
  • 483 Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 2157)

Abstract

In this chapter we elaborate on Hilbert–Schmidt and trace class integral operators, the noncommutative Hölder inequality for Schatten–von Neumann ideals, and particularly, trace ideal estimates for operators consisting of various products of operators of multiplication and resolvents of the Laplacian in \(L^{2}(\mathbb{R}^{n})\).

Keywords

Trace Class Integral Operator Technical Chapters Fourier Multiplier Complex Interpolation Well-known Characterization 
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References

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    C. Callias, Axial anomalies and index theorems on open spaces. Commun. Math. Phys. 62, 213–234 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
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    B. Simon, Trace Ideals and Their Applications, 2nd edn. Mathematical Surveys and Monographs, Vol. 120 (Amer. Math. Soc., Providence, RI, 2005)Google Scholar
  3. 99.
    H. Vogt, A Hilbert-Schmidt criterion for the product of multiplication and convolution operators. Preprint (2015)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Fritz Gesztesy
    • 1
  • Marcus Waurick
    • 2
  1. 1.Dept of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Institut für AnalysisTU DresdenDresdenGermany

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