Uniform Kadec-Klee property and nearly uniform convexity in Köthe-Bochner sequence spaces

Kolwicz, Paweł

Bollettino dell'Unione Matematica Italiana, Tome 6-A (2003), p. 221-235 / Harvested from Biblioteca Digitale Italiana di Matematica

Abstract

The uniformly Kadec-Klee property in Köthe-Bochner sequence spaces $E(X)$, where $E$ is a Köthe sequence space and $X$ is an arbitrary separable Banach space, is studied. Namely, the question of whether or not this geometric property lifts from $X$ and $E$ to $E(X)$ is examined. It is settled affirmatively in contrast to the case when $E$ is a Köthe function space. As a corollary we get criteria for $E(X)$ to be nearly uniformly convex.

Résumé

Viene studiata la proprietà uniforme di Kadec-Klee in spazi sequenziali di Kothe-Bochner $E(X)$, dove $E$ è uno spazio sequenziale di Kothe e $X$ è un arbitrario spazio di Banach separabile. Precisamente, viene esaminato il problema se questa proprietà geometrica si può trasportare da $X$ in $E(X)$. Ciò viene stabilito in contrasto con il caso in cui $E$ è uno spazio di Kothe. Come corollario viene stabilito un criterio affichè $E(X)$ sia «nearly» uniformemente convesso.

Détail

Publié le : 2003-02-01

MR 1955707 | Zbl 1178.46008

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