Results in Mathematics

, Volume 39, Issue 3–4, pp 201–217 | Cite as

Minimal ideals of n-homogeneous polynomials on Banach spaces



The minimal kernel of a p-Banach ideal of n-homogeneous polynomials between Banach spaces is defined as a composition ideal, characterized to be the smallest ideal which coincides with the given one on finite-dimensional spaces and represented through tensor products with appropriate norms.

Mathematics Subject Classification 2000

46G25 46G20 46B28 


Ideals of polynomials tensor norm symmetric tensor product 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AS]
    R. Aron — M. Schottenloher, Compact holomorphic mappings on Banach spaces and the approximation property, J. Funct. Analysis 21 (1976) 7–30.MathSciNetMATHCrossRefGoogle Scholar
  2. [B]
    H. Braunss, Multi-ideals with special properties, Potsdamer Forschungen, 1987, Nr. 1.Google Scholar
  3. [BJ1]
    H. Braunss — H. Junek, Bilinear mappings and operator ideals, Potsdamer Forschungen, 1985, Nr. 1.Google Scholar
  4. [BJ2]
    H. Braunss — H. Junek, On types of polynomials and holomorphic functions on Banach spaces, Note di Matematica 10 (1990) 47–58.MathSciNetMATHGoogle Scholar
  5. [C]
    P. Casazza, Approximation properties, to appear in: Handbook of Banach spaces.Google Scholar
  6. [De]
    A. Defant, Produkte von Tensornormen, Habilitationsschrift, Oldenburg, 1986.Google Scholar
  7. [Di]
    S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer Monogr. Math., 1999.Google Scholar
  8. [DF]
    A. Defant — K. Floret, Tensor Norms and Operator Ideals, North Holland Math. Studies 176, 1993.Google Scholar
  9. [F1]
    K. Floret, Natural norms on symmetric tensor products of normed spaces, Note di Matematica 17 (1997) 153–188.MathSciNetMATHGoogle Scholar
  10. [F2]
    K. Floret, The extension theorem for norms on symmetric tensor products of normed spaces, preprint 1999.Google Scholar
  11. [F3]
    K. Floret, On ideals of n-homogeneous polynomials on Banach spaces, to appear in: Proc. in honour of A. Mallios, Athens, 1999.Google Scholar
  12. [F4]
    K. Floret, The metric theory of symmetric tensor products of normed spaces, in preparation.Google Scholar
  13. [FG]
    K. Floret — D. García, On ideals of polynomials and multilinear mappings between Banach spaces, preprint 2000.Google Scholar
  14. [FH]
    K. Floret — S. Hunfeld, Ultrastability of ideals of homogeneous polynomials and multilinear mappings on Banach spaces, to appear in: Proc. Amer. Math. Soc.Google Scholar
  15. [M]
    B. Maurey, Théorèmes de factorization pour les opérateurs linéaires à valeurs dans les espaces L p, Astérisque 11, 1974.Google Scholar
  16. [M1]
    M. Matos, On multilinear mappings of nuclear type, Revista Math. Univ. Complut. Madrid 6 (1993) 61–81.MathSciNetMATHGoogle Scholar
  17. [M2]
    M. Matos, Absolutely summing holomorphic mappings, An. Acad. bras. Ci. 68 (1996) 1–13.MathSciNetMATHGoogle Scholar
  18. [N]
    L. Nachbin, Topology on Spaces of Holomorphic Mappings, Ergebn. Math. u. Grenzgeb. 47, Springer, 1969.Google Scholar
  19. [P1]
    A. Pietsch, Operator Ideals, Dtsch. Verlag d. Wissenschaften Berlin, 1978, and North Holland Math. Library, 1980.Google Scholar
  20. [P2]
    A. Pietsch, Ideals of multilinear functional, Proc. 2nd Int. Conf. Operator Alg. etc. Leipzig, Teubner Texte Math. 62 (1983) 185–199.Google Scholar
  21. [W]
    Chr. Waltz, Adjungierte Polynomiale und duale Typen auf Banachräumen und ihre Anwendungen, Dissertation, Potsdam, 1994.Google Scholar

Copyright information

© Birkhäuser Verlag, Basel 2001

Authors and Affiliations

  1. 1.Fachbereich Mathematikder UniversitätOldenburg

Personalised recommendations