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A Composition Theorem for Multiple Summing Operators

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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.

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References

  • R Alencar (1985) ArticleTitleMultilinear mappings of nuclear and integral type. Proc Amer Math Soc 94 33–38

    Google Scholar 

  • F Bombal D Pérez-García I Villanueva (2004) ArticleTitleMultilinear extensions of Grothendieck’s theorem. Quarterly J Math 55 441–450 Occurrence Handle10.1093/qjmath/55.4.441

    Article  Google Scholar 

  • Defant A, Floret K (1993) Tensor Norms and Operator Ideals. Amsterdam: North-Holland

  • Diestel J, Jarchow H, Tonge A (1995) Absolutely Summing Operators. Cambridge: Univ Press

  • Diestel J, Uhl JJ (1977) Vector Measures. Providence, RI: Amer Math Soc

  • Dineen S (1981) Complex Analysis in Locally Convex Spaces. Amsterdam: North-Holland

  • Grothendieck A (1955) Produits tensoriels topologiques et espaces nucléaires. Mem Amer Math Soc 16

  • MC Matos (2003) ArticleTitleFully absolutely summing and Hilbert-Schmidt multilinear mappings. Collect Math 54 111–136

    Google Scholar 

  • D Pérez-García (2004) ArticleTitleThe inclusion theorem for multiple summing operators. Studia Math 165 275–290

    Google Scholar 

  • D Pérez-García I Villanueva (2003) ArticleTitleMultiple summing operators on Banach spaces. J Math Anal Appl 285 86–96 Occurrence Handle10.1016/S0022-247X(03)00352-4

    Article  Google Scholar 

  • D Pérez-García I Villanueva (2004) ArticleTitleMultiple summing operators on C(K) spaces. Ark Mat 42 153–171

    Google Scholar 

  • I Villanueva (2003) ArticleTitleIntegral mappings between Banach spaces. J Math Anal Appl 279 56–70 Occurrence Handle10.1016/S0022-247X(02)00362-1

    Article  Google Scholar 

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Authors and Affiliations

  1. Universidad Complutense de Madrid, Spain

    David Pérez-García & Ignacio Villanueva

Authors
  1. David Pérez-García
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  2. Ignacio Villanueva
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Both authors were partially supported by DGICYT grant BMF2001-1284.

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Pérez-García, D., Villanueva, I. A Composition Theorem for Multiple Summing Operators. Mh Math 146, 257–261 (2005). https://doi.org/10.1007/s00605-005-0316-1

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  • DOI: https://doi.org/10.1007/s00605-005-0316-1

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