We obtain a classification of projective tensor products of C(K) spaces according to whether none, exactly one or more than one factor contains copies of ℓ₁, in terms of the behaviour of certain classes of multilinear operators on the product of the spaces or the verification of certain Banach space properties of the corresponding tensor product. The main tool is an improvement of some results of Emmanuele and Hensgen on the reciprocal Dunford-Pettis and Pełczyński's (V) properties of the projective tensor product of Banach spaces. We also study relationships between several classes of multilinear operators and the associated linear operators.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm148-3-5,
author = {Fernando Bombal and Maite Fern\'andez and Ignacio Villanueva},
title = {Some classes of multilinear operators on C(K) spaces},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {259-273},
zbl = {0995.46015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm148-3-5}
}
Fernando Bombal; Maite Fernández; Ignacio Villanueva. Some classes of multilinear operators on C(K) spaces. Studia Mathematica, Tome 147 (2001) pp. 259-273. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm148-3-5/