Results in Mathematics

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

Minimal ideals of n-homogeneous polynomials on Banach spaces

  • Klaus Floret


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 


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  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

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