We study property (β) in Köthe-Bochner sequence spaces E(X), where E is any Köthe sequence space and X is an arbitrary Banach space. The question of whether or not this geometric property lifts from X and E to E(X) is examined. We prove that if dim X = ∞, then E(X) has property (β) if and only if X has property (β) and E is orthogonally uniformly convex. It is also showed that if dim X < ∞, then E(X) has property (β) if and only if E has property (β). Our results essentially extend and improve those from [14] and [15].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm162-3-1,
author = {Henryk Hudzik and Pawe\l\ Kolwicz},
title = {On property ($\beta$) of Rolewicz in K\"othe-Bochner sequence spaces},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {195-212},
zbl = {1057.46018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm162-3-1}
}
Henryk Hudzik; Paweł Kolwicz. On property (β) of Rolewicz in Köthe-Bochner sequence spaces. Studia Mathematica, Tome 162 (2004) pp. 195-212. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm162-3-1/