Let X be a Banach space and 1 < p, p' < infinity such that 1/p + 1/p' = 1. Then L-p[0,1]circle times X, respectively L-p[0,1]circle times X, the projective, respectively injective, tensor product of L-p[0,1] and X, is a Grothendieck space if and only if X is a Grothendieck space and each continuous linear operator front L-p[0,1], respectively L-p'[0, 1], to X*, respectively X**, is compact.
The projective and injective tensor products of $L^p[0,1]$ and X being Grothendieck spaces
EMMANUELE, Giovanni
2005-01-01
Abstract
Let X be a Banach space and 1 < p, p' < infinity such that 1/p + 1/p' = 1. Then L-p[0,1]circle times X, respectively L-p[0,1]circle times X, the projective, respectively injective, tensor product of L-p[0,1] and X, is a Grothendieck space if and only if X is a Grothendieck space and each continuous linear operator front L-p[0,1], respectively L-p'[0, 1], to X*, respectively X**, is compact.File in questo prodotto:
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