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On certain subsets of Bochner integrable function spaces.

Fernando Bombal — 1991

Extracta Mathematicae

One of the most important methods used in literature to introduce new properties in a Banach space E, consists in establishing some non trivial relationships between different classes of subsets of E. For instance, E is reflexive, or has finite dimension, if and only if every bounded subset is weakly relatively compact or norm relatively compact, respectively. On the other hand, Banach spaces of the type C(K) and Lp(μ) play a vital role in the general theory of Banach...

Some classes of multilinear operators on C(K) spaces

Fernando BombalMaite FernándezIgnacio Villanueva — 2001

Studia Mathematica

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...

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