The projective tensor product (II): the Radon-Nikodym property.

Diestel, Joe, Fourie, Jan, and Swart, Johan. "The projective tensor product (II): the Radon-Nikodym property.." RACSAM 100.1-2 (2006): 75-100. <http://eudml.org/doc/41644>.

@article{Diestel2006,
abstract = {In this paper we discuss the problem of when the projective tensor product of two Banach spaces has the Radon-Nikodym property. We give a detailed exposition of the famous examples of Jean Bourgain and Gilles Pisier showing that there are Banach spaces X and Y such that each has the Radon-Nikodym property but for which their projective tensor product does not; this result depends on the classical theory of absolutely summing, integral and nuclear operators, as well as the famous Grothendieck inequality for its punch-line. In the last section of this paper we discuss many results of a positive character, due to Qingying Bu and various of his coauthors; in particular, we mention results of Bu, Diestel, Dowling and Oja to the effect that if one of the spaces has a boundedly complete FDD then the projective tensor product of two spaces with the RNP has it and a modification of a result of Bu and Pei-Kee Lin to the effect that if X is a Banach lattice with RNP and Y is any Banach space with RNP then their projective product has RNP.},
author = {Diestel, Joe, Fourie, Jan, Swart, Johan},
journal = {RACSAM},
keywords = {projective tensor product; Radon-Nikodym property; Bourgain-Pisier space; Banach lattice},
language = {eng},
number = {1-2},
pages = {75-100},
title = {The projective tensor product (II): the Radon-Nikodym property.},
url = {http://eudml.org/doc/41644},
volume = {100},
year = {2006},
}

TY - JOUR
AU - Diestel, Joe
AU - Fourie, Jan
AU - Swart, Johan
TI - The projective tensor product (II): the Radon-Nikodym property.
JO - RACSAM
PY - 2006
VL - 100
IS - 1-2
SP - 75
EP - 100
AB - In this paper we discuss the problem of when the projective tensor product of two Banach spaces has the Radon-Nikodym property. We give a detailed exposition of the famous examples of Jean Bourgain and Gilles Pisier showing that there are Banach spaces X and Y such that each has the Radon-Nikodym property but for which their projective tensor product does not; this result depends on the classical theory of absolutely summing, integral and nuclear operators, as well as the famous Grothendieck inequality for its punch-line. In the last section of this paper we discuss many results of a positive character, due to Qingying Bu and various of his coauthors; in particular, we mention results of Bu, Diestel, Dowling and Oja to the effect that if one of the spaces has a boundedly complete FDD then the projective tensor product of two spaces with the RNP has it and a modification of a result of Bu and Pei-Kee Lin to the effect that if X is a Banach lattice with RNP and Y is any Banach space with RNP then their projective product has RNP.
LA - eng
KW - projective tensor product; Radon-Nikodym property; Bourgain-Pisier space; Banach lattice
UR - http://eudml.org/doc/41644
ER -