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Cotype of operators fromC(K)

Authors:	Michel Talagrand

Affiliation:	(1) Equipe d'Analyse Tour 46 U.A. au C.N.R.S. no 754, Université Paris VI, 4 Place Jussieu, F-75230 Paris;(2) Department of Mathematics, The Ohio State University, 231 W. 18th Avenue, 43210 Columbus, Ohio, USA

Abstract:	Summary Forq>2, an operator fromC(K) toX is of cotypeq if and only if it factors through the Lorentz space $L_{t^q (log t)^{q/2} ,1} (mu )$ . Forq=2, ifX is a rearrangement invariant space on [0, 1], the injectionC([0, 1])X is of cotype 2 if and only if it factors through the Lorentz space $L_{t^2 log t,2} ([0,1])$ ; but there is a cotype 2 operator C(K) that does not factor through $L_{t^2 log t,2} (mu )$ . If a Banach latticeX satisfies the Orlicz property, any bounded lattice operatorT:C(K)X is of cotype 2. We however construct a Banach lattice with the Orlicz property, but that fails to be of cotype 2.Oblatum 4-VII-1990 & 18-IV-1991Work partially supported by an NSF grant

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