Skip to main content
SpringerLink
Log in

Besov Spaces and a Trace Ideal

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

Let Π2 be the operator ideal of all absolutely 2-summing operators and let (Π2)2,1(a) be the ideal of operators of Π2-approximation type l2,1. In this paper we give some sufficient conditions for matrices and kernels related to Besov spaces to generate operators belonging to the ideal (Π2)2,1(a).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Bergh and J. Lofstrom, Interpolation Spaces, Springer-Verlag (Berlin, Heidelberg and New York, 1976).

    Google Scholar 

  2. M. S. Birman and M. Z. Solomyak, Estimates of singular numbers of integral operators, Russian Math. Surveys, 32 (1977), 15–89.

    Google Scholar 

  3. B. Carl, Inequalities between absolutely (p, q)-summing norms, Studia Math., 69 (1980), 143–148.

    Google Scholar 

  4. J. A. Cochran, The nuclearity of operators generated by Holder continuous kernels, Proc. Cambridge Philos. Soc., 75 (1974), 351–356.

    Google Scholar 

  5. J. A. Cochran, Composite integral operators and nuclearity, Ark. Mol. 15 (1977), 215–222.

    Google Scholar 

  6. A. Grothendieck, La theorie de Fredholm, Bull. Soc. Math. France, 84 (1956), 319–384.

    Google Scholar 

  7. H. Konig, Eigenvalue Distribution of Compact Operators, Birkhauser (Basel, 1986).

    Google Scholar 

  8. J. S. Martins, Approximation numbers of maps on Besov sequence spaces, J. London Math. Soc., 40 (1989), 120–136.

    Google Scholar 

  9. A. Pietsch, Eigenvalues of integral operators. I. Math. Ann., 247 (1980), 169–178.

    Google Scholar 

  10. A. Pietsch, Operator ideals with a trace, Math. Nachr., 100 (1981), 61–91.

    Google Scholar 

  11. A. Pietsch, Approximation spaces, J. Approx. Theory, 32 (1981), 115–134.

    Google Scholar 

  12. A. Pietsch, Eigenvalues and s-numbers, Cambridge Univ. Press (Cambridge, 1987).

    Google Scholar 

  13. A. Pietsch, Operator Ideals, North-Holland (Amsterdam, New York and Oxford, 1980).

    Google Scholar 

  14. W. F. Stinespring, A sufficient condition for an integral operator to have a trace, J. Reine Angew. Math., 200 (1958), 200–207.

    Google Scholar 

  15. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland (Amsterdam, New York and Oxford, 1978).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Análisis Matemático Campus Universitario Sur, Universidad de Santiago de Compostela Facultad de Matemáticas, 15706, Santiago de Compostela, Spain

    M.A. Fugarolas

Authors
  1. M.A. Fugarolas
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fugarolas, M. Besov Spaces and a Trace Ideal. Acta Mathematica Hungarica 82, 75–81 (1999). https://doi.org/10.1023/A:1026429420161

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1026429420161

Keywords

Search

Navigation