Uniform Kadec-Klee property and nearly uniform convexity in Köthe-Bochner sequence spaces
Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 1, pp. 221-235
Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica
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.
@article{BUMI_2003_8_6B_1_a13,
author = {Kolwicz, Pawe{\l}},
title = {Uniform {Kadec-Klee} property and nearly uniform convexity in {K\"othe-Bochner} sequence spaces},
journal = {Bollettino della Unione matematica italiana},
pages = {221--235},
publisher = {mathdoc},
volume = {Ser. 8, 6B},
number = {1},
year = {2003},
zbl = {1178.46008},
mrnumber = {MR1955707},
language = {en},
url = {http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_1_a13/}
}
TY - JOUR AU - Kolwicz, Paweł TI - Uniform Kadec-Klee property and nearly uniform convexity in Köthe-Bochner sequence spaces JO - Bollettino della Unione matematica italiana PY - 2003 SP - 221 EP - 235 VL - 6B IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_1_a13/ LA - en ID - BUMI_2003_8_6B_1_a13 ER -
%0 Journal Article %A Kolwicz, Paweł %T Uniform Kadec-Klee property and nearly uniform convexity in Köthe-Bochner sequence spaces %J Bollettino della Unione matematica italiana %D 2003 %P 221-235 %V 6B %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_1_a13/ %G en %F BUMI_2003_8_6B_1_a13
Kolwicz, Paweł. Uniform Kadec-Klee property and nearly uniform convexity in Köthe-Bochner sequence spaces. Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 1, pp. 221-235. http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_1_a13/