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Eigenvalues of Operators on Banach Spaces

  • Hermann König
Part of the Operator Theory: Advances and Applications book series (OT, volume 16)

Abstract

The q-nuclear operators Nq, q- and (q,2)-summing operators πq and πq,2 as well as the s-number ideals S q a and S q x coincide with Schatten classes Sp (H) on Hilbert spaces H, for appropriate values of p = p(q) (1.d.12). Thus they form extensions of the Schatten classes to operator ideals on (all) Banach spaces. On a fixed Banach space, all maps in these ideals are power-compact and hence Riesz operators (1.a.5). By Weyl’s inequality (1.b.9), Sp(H)-operators have p-th power summable eigenvalues. It is thus natural to ask: What is the optimal order of summability of the eigenvalues of the above classes of operators on Banach spaces? This is the main topic of this chapter: we extend Weyl’s inequality to the above operator ideals on Banach spaces.

Keywords

Hilbert Space Banach Space Banach Lattice Diagonal Operator Entropy Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 1986

Authors and Affiliations

  • Hermann König
    • 1
  1. 1.Mathematisches InstitutUniversität KielKiel 1Germany

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