Cotype of operators fromC(K) |
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Authors: | Michel Talagrand |
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Institution: | (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 |
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Abstract: | Summary Forq>2, an operator fromC(K) toX is of cotypeq if and only if it factors through the Lorentz space
. 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
; but there is a cotype 2 operator C(K) ![ell](/content/j02503148355l5t3/xxlarge8467.gif) that does not factor through
. 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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