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

Paweł Kolwicz

Bollettino dell'Unione Matematica Italiana (2003)

  • Volume: 6-B, Issue: 1, page 221-235
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Kolwicz, Paweł. "Uniform Kadec-Klee property and nearly uniform convexity in Köthe-Bochner sequence spaces." Bollettino dell'Unione Matematica Italiana 6-B.1 (2003): 221-235. <http://eudml.org/doc/196023>.

@article{Kolwicz2003,
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.},
author = {Kolwicz, Paweł},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {221-235},
publisher = {Unione Matematica Italiana},
title = {Uniform Kadec-Klee property and nearly uniform convexity in Köthe-Bochner sequence spaces},
url = {http://eudml.org/doc/196023},
volume = {6-B},
year = {2003},
}

TY - JOUR
AU - Kolwicz, Paweł
TI - Uniform Kadec-Klee property and nearly uniform convexity in Köthe-Bochner sequence spaces
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/2//
PB - Unione Matematica Italiana
VL - 6-B
IS - 1
SP - 221
EP - 235
AB - 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.
LA - eng
UR - http://eudml.org/doc/196023
ER -

References

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