We prove that the Musielak-Orlicz sequence space with the Orlicz norm has property (β) iff it is reflexive. It is a generalization and essential extension of the respective results from [3] and [5]. Moreover, taking an arbitrary Musielak-Orlicz function instead of an N-function we develop new methods and techniques of proof and we consider a wider class of spaces than in [3] and [5].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc68-0-9,
author = {Pawe\l\ Kolwicz},
title = {On property ($\beta$) of Rolewicz in Musielak-Orlicz sequence spaces equipped with the Orlicz norm},
journal = {Banach Center Publications},
volume = {68},
year = {2005},
pages = {79-86},
zbl = {1087.46010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc68-0-9}
}
Paweł Kolwicz. On property (β) of Rolewicz in Musielak-Orlicz sequence spaces equipped with the Orlicz norm. Banach Center Publications, Tome 68 (2005) pp. 79-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc68-0-9/