Israel Journal of Mathematics

, Volume 79, Issue 2–3, pp 331–365

A grothendieck factorization theorem on 2-convex schatten spaces

  • Françoise Lust-Piquard
Article

Abstract

We prove that for every bounded linear operatorT:C2pH(1≤p<∞,H is a Hilbert space,C2pp is the Schatten space) there exists a continuous linear formf onCp such thatf≥0, ‖f‖(CCp)*=1 and
$$\forall x \in C^{2p} , \left\| {T(x)} \right\| \leqslant 2\sqrt 2 \left\| T \right\|< f\frac{{x * x + xx*}}{2} > 1/2$$
. Forp=∞ this non-commutative analogue of Grothendieck’s theorem was first proved by G. Pisier. In the above statement the Schatten spaceC2p can be replaced byEE2 whereE(2) is the 2-convexification of the symmetric sequence spaceE, andf is a continuous linear form onCE. The statement can also be extended toLE{(su2)}(M, τ) whereM is a Von Neumann algebra,τ a trace onM, E a symmetric function space.

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Copyright information

© Hebrew University 1992

Authors and Affiliations

  • Françoise Lust-Piquard
    • 1
  1. 1.CNRS-UA D 0757Université de Paris-Sud MathématiquesOrsay CedexFrance

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