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Fonctionnelles analytiques sur certains espaces de Banach

Gérard Cœuré (1971)

Annales de l'institut Fourier

Il est démontré que l’espace des fonctions holomorphes sur un sous-espace homogène E , au sens de Katznelson, de L 1 ( π ) muni de la topologie engendrée par les semi-normes portées par les compacts de E , est bornologique.

Fragmentability and compactness in C(K)-spaces

B. Cascales, G. Manjabacas, G. Vera (1998)

Studia Mathematica

Let K be a compact Hausdorff space, C p ( K ) the space of continuous functions on K endowed with the pointwise convergence topology, D ⊂ K a dense subset and t p ( D ) the topology in C(K) of pointwise convergence on D. It is proved that when C p ( K ) is Lindelöf the t p ( D ) -compact subsets of C(K) are fragmented by the supremum norm of C(K). As a consequence we obtain some Namioka type results and apply them to prove that if K is separable and C p ( K ) is Lindelöf, then K is metrizable if, and only if, there is a countable and dense...

Fragmentability of the Dual of a Banach Space with Smooth Bump

Kortezov, I. (1998)

Serdica Mathematical Journal

We prove that if a Banach space X admits a Lipschitz β-smooth bump function, then (X ∗ , weak ∗ ) is fragmented by a metric, generating a topology, which is stronger than the τβ -topology. We also use this to prove that if X ∗ admits a Lipschitz Gateaux-smooth bump function, then X is sigma-fragmentable.

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