Some classes of multilinear operators on C(K) spaces

Fernando Bombal, Maite Fernández, and Ignacio Villanueva. "Some classes of multilinear operators on C(K) spaces." Studia Mathematica 148.3 (2001): 259-273. <http://eudml.org/doc/284504>.

@article{FernandoBombal2001,
abstract = {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.},
author = {Fernando Bombal, Maite Fernández, Ignacio Villanueva},
journal = {Studia Mathematica},
keywords = {classification of projective tensor product; multilinear operators},
language = {eng},
number = {3},
pages = {259-273},
title = {Some classes of multilinear operators on C(K) spaces},
url = {http://eudml.org/doc/284504},
volume = {148},
year = {2001},
}

TY - JOUR
AU - Fernando Bombal
AU - Maite Fernández
AU - Ignacio Villanueva
TI - Some classes of multilinear operators on C(K) spaces
JO - Studia Mathematica
PY - 2001
VL - 148
IS - 3
SP - 259
EP - 273
AB - 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.
LA - eng
KW - classification of projective tensor product; multilinear operators
UR - http://eudml.org/doc/284504
ER -