On property (β) of Rolewicz in Köthe-Bochner sequence spaces

Henryk Hudzik, and Paweł Kolwicz. "On property (β) of Rolewicz in Köthe-Bochner sequence spaces." Studia Mathematica 162.3 (2004): 195-212. <http://eudml.org/doc/285157>.

@article{HenrykHudzik2004,
abstract = {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].},
author = {Henryk Hudzik, Paweł Kolwicz},
journal = {Studia Mathematica},
keywords = {Köthe-Bochner spaces; orthogonal uniform convexity; Orlicz space; uniform monotonicity},
language = {eng},
number = {3},
pages = {195-212},
title = {On property (β) of Rolewicz in Köthe-Bochner sequence spaces},
url = {http://eudml.org/doc/285157},
volume = {162},
year = {2004},
}

TY - JOUR
AU - Henryk Hudzik
AU - Paweł Kolwicz
TI - On property (β) of Rolewicz in Köthe-Bochner sequence spaces
JO - Studia Mathematica
PY - 2004
VL - 162
IS - 3
SP - 195
EP - 212
AB - 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].
LA - eng
KW - Köthe-Bochner spaces; orthogonal uniform convexity; Orlicz space; uniform monotonicity
UR - http://eudml.org/doc/285157
ER -