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Factorization of operator valued Lp for 0 ≤ p < 1

✍ Scribed by Lahcène Mezrag

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
152 KB
Volume
266
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In [5], it is proved that a bounded linear operator u, from a Banach space Y into an L~p~(S, ν) factors through L~__p__1~ (S, ν) for some p~1~ > 1, if Y* is of finite cotype; (S, ν) is a probability space for p = 0, and any measure space for 0 < p < 1. In this paper, we generalize this result to uv, where u : Y → L~p~(S, ν) and v : X → Y are linear operators such that v* is of finite Kašin cotype. This result gives also a new proof of Grothendieck's theorem. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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