Advertisement

Monatshefte für Mathematik

, Volume 146, Issue 3, pp 257–261 | Cite as

A Composition Theorem for Multiple Summing Operators

  • David Pérez-García
  • Ignacio Villanueva
Article

Abstract.

We prove that the composition S(u1, …, u n ) of a multilinear multiple 2-summing operator S with 2-summing linear operators u j is nuclear, generalizing a linear result of Grothendieck.

2000 Mathematics Subject Classifications: 47H60, 46B25 
Key words: Multilinear operators, multiple p-summing operators, nuclear operators 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alencar, R 1985Multilinear mappings of nuclear and integral type.Proc Amer Math Soc943338Google Scholar
  2. Bombal, F, Pérez-García, D, Villanueva, I 2004Multilinear extensions of Grothendieck’s theorem.Quarterly J Math55441450CrossRefGoogle Scholar
  3. Defant A, Floret K (1993) Tensor Norms and Operator Ideals. Amsterdam: North-HollandGoogle Scholar
  4. Diestel J, Jarchow H, Tonge A (1995) Absolutely Summing Operators. Cambridge: Univ PressGoogle Scholar
  5. Diestel J, Uhl JJ (1977) Vector Measures. Providence, RI: Amer Math SocGoogle Scholar
  6. Dineen S (1981) Complex Analysis in Locally Convex Spaces. Amsterdam: North-HollandGoogle Scholar
  7. Grothendieck A (1955) Produits tensoriels topologiques et espaces nucléaires. Mem Amer Math Soc 16Google Scholar
  8. Matos, MC 2003Fully absolutely summing and Hilbert-Schmidt multilinear mappings.Collect Math54111136Google Scholar
  9. Pérez-García, D 2004The inclusion theorem for multiple summing operators.Studia Math165275290Google Scholar
  10. Pérez-García, D, Villanueva, I 2003Multiple summing operators on Banach spaces.J Math Anal Appl2858696CrossRefGoogle Scholar
  11. Pérez-García, D, Villanueva, I 2004Multiple summing operators on C(K) spaces.Ark Mat42153171Google Scholar
  12. Villanueva, I 2003Integral mappings between Banach spaces.J Math Anal Appl2795670CrossRefGoogle Scholar

Copyright information

© Springer-Verlag/Wien 2005

Authors and Affiliations

  • David Pérez-García
    • 1
  • Ignacio Villanueva
    • 1
  1. 1.Universidad Complutense de MadridSpain

Personalised recommendations