Some classes of multilinear operators on $C(K)$ spaces
Studia Mathematica, Tome 148 (2001) no. 3, pp. 259-273
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $\ell _1$, 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 Pe/lczyński'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.
Keywords:
obtain classification projective tensor products spaces according whether none exactly factor contains copies ell terms behaviour certain classes multilinear operators product spaces verification certain banach space properties corresponding tensor product main tool improvement results emmanuele hensgen reciprocal dunford pettis lczy skis properties projective tensor product banach spaces study relationships between several classes multilinear operators associated linear operators
Affiliations des auteurs :
Fernando Bombal 1 ; Maite Fernández 2 ; Ignacio Villanueva 3
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author = {Fernando Bombal and Maite Fern\'andez and Ignacio Villanueva},
title = {Some classes of multilinear operators on $C(K)$ spaces},
journal = {Studia Mathematica},
pages = {259--273},
publisher = {mathdoc},
volume = {148},
number = {3},
year = {2001},
doi = {10.4064/sm148-3-5},
language = {en},
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Fernando Bombal; Maite Fernández; Ignacio Villanueva. Some classes of multilinear operators on $C(K)$ spaces. Studia Mathematica, Tome 148 (2001) no. 3, pp. 259-273. doi: 10.4064/sm148-3-5
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