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Maurey’s factorization theory for operator spaces

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Abstract

We prove an operator space version of Maurey’s theorem, which claims that every absolutely (p, 1)-summing map on C(K) is automatically absolutely q-summing for q > p. Our results imply in particular that every completely bounded map from B(H) with values in Pisier’s operator space OH is completely p-summing for p > 2. This fails for p = 2. As applications, we obtain eigenvalue estimates for translation invariant maps defined on the von Neumann algebra V N(G) associated with a discrete group G. We also develop a notion of cotype which is compatible with factorization results on noncommutative L p spaces.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green St, Urbana, IL, 61891, USA

    Marius Junge

  2. Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas, Serrano 121, 28006, Madrid, Spain

    Javier Parcet

Authors
  1. Marius Junge
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  2. Javier Parcet
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Correspondence to Marius Junge.

Additional information

Junge is partially supported by the NSF DMS-0556120 (and NSF DMS and DMS-0901457). Parcet is partially supported by ‘Programa Ramón y Cajal 2005’ and by Grants MTM2007-60952 and CCG07-UAM/ESP-1664, Spain.

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Junge, M., Parcet, J. Maurey’s factorization theory for operator spaces. Math. Ann. 347, 299–338 (2010). https://doi.org/10.1007/s00208-009-0440-7

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  • DOI: https://doi.org/10.1007/s00208-009-0440-7

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