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Inequalities between geometric quantities of operators in Banach spaces

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Abstract

Relations concerning entropy quantities and s-numbers are established. In particular, we derive inequalities between entropy numbers and Weyl numbers. Furthermore, we give eigenvalue distributions for operators of lp,u-type.

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References

  1. Carl. B.: Entropy numbers, s-numbers, and eigenvalue problems, J. Functional Analysis (to appear).

  2. --: Entropy-function and eigenvalues.

  3. Carl,B. and Triebel, H.: Inequalities between eigenvalues, entropy numbers and related quantities of compact operators in Banach spaces, Math. Ann. 251, 129–133 (1980).

    Google Scholar 

  4. Höllig, K.: Diameters of classes of smooth functions, preprint, Bonn 1979.

  5. Johnson, W.B. and König, H. and Maurey, B. and Retherford, J.R.: Eigenvalues of p-summing and lp-type operators in Banach Spaces, J. Functional Anal. 32, 353–380 (1979).

    Google Scholar 

  6. König, H. and Retherford, J.R. and Tomczak-Jaegermann, N.: On the eigenvalues of (p,2)-summing operators and constants associated to normed spaces, J. Functional Anal.

  7. ——: A formula for the eigenvalues of a compact operator, Studia Math. 65, 141–146 (1979).

    Google Scholar 

  8. Pietsch,A.:Operator ideals, Berlin, 1978.

  9. --:s-numbers of operators in Banach spaces, Studia Math. (51), 201–223 (1974).

  10. ——:Weyl numbers and eigenvalues of operators in Banach spaces, Math. Ann. 247, 149–168 (1980).

    Google Scholar 

  11. ——:Eigenvalues of integral operators I, Math.Ann. 247, 169–178 (1980).

    Google Scholar 

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Authors and Affiliations

  1. Sektion Mathematik, Universität Jena, 69 Jena, DDR

    Bernd Carl

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  1. Bernd Carl
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Carl, B. Inequalities between geometric quantities of operators in Banach spaces. Integr equ oper theory 5, 759–773 (1982). https://doi.org/10.1007/BF01694062

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  • DOI: https://doi.org/10.1007/BF01694062

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