Geodesic
Some classes of multilinear operators on $C(K)$ spaces
Fernando Bombal 1   ; Maite Fernández 2   ; Ignacio Villanueva 3
1 Departamento de Análisis Matemático Facultad de Matemáticas Universidad Complutense de Madrid Madrid 28040, Spain
2 CIMAT, A.P. 402 Guanajuato, Gto. 36000, México
3 Departamento de Análisis Matemático Facultad de Matemáticas Universidad Complutense de Madrid Madrid 28040
Studia Mathematica, Tome 148 (2001) no. 3, pp. 259-273 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm148-3-5
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

Fernando Bombal  1   ; Maite Fernández  2   ; Ignacio Villanueva  3

1 Departamento de Análisis Matemático Facultad de Matemáticas Universidad Complutense de Madrid Madrid 28040, Spain
2 CIMAT, A.P. 402 Guanajuato, Gto. 36000, México
3 Departamento de Análisis Matemático Facultad de Matemáticas Universidad Complutense de Madrid Madrid 28040 
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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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