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Some classes of multilinear operators on C(K) spaces

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Bombal F., Fernández M., Villanueva I.
Studia Mathematica
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2001
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tom 148
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nr 3
259-273
EN
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.
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Factorizing multilinear operators on Banach spaces, C*-algebras and JB*-triples

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Palazuelos C., Peralta A., Villanueva I.
Studia Mathematica
|
2009
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tom 192
|
nr 2
129-146
EN
In recent papers, the Right and the Strong* topologies have been introduced and studied on general Banach spaces. We characterize different types of continuity for multilinear operators (joint, uniform, etc.) with respect to the above topologies. We also study the relations between them. Finally, in the last section, we relate the joint Strong*-to-norm continuity of a multilinear operator T defined on C*-algebras (respectively, JB*-triples) to C*-summability (respectively, JB*-triple-summability).
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