Mathematische Annalen

, Volume 347, Issue 2, pp 299–338

Maurey’s factorization theory for operator spaces

Article

DOI: 10.1007/s00208-009-0440-7

Cite this article as:
Junge, M. & Parcet, J. Math. Ann. (2010) 347: 299. doi:10.1007/s00208-009-0440-7

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 VN(G) associated with a discrete group G. We also develop a notion of cotype which is compatible with factorization results on noncommutative Lp spaces.

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Instituto de Ciencias MatemáticasCSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones CientíficasMadridSpain