The property ( β ) of Orlicz-Bochner sequence spaces

Paweł Kolwicz

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 1, page 119-132
  • ISSN: 0010-2628

Abstract

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A characterization of property ( β ) of an arbitrary Banach space is given. Next it is proved that the Orlicz-Bochner sequence space l Φ ( X ) has the property ( β ) if and only if both spaces l Φ and X have it also. In particular the Lebesgue-Bochner sequence space l p ( X ) has the property ( β ) iff X has the property ( β ) . As a corollary we also obtain a theorem proved directly in [5] which states that in Orlicz sequence spaces equipped with the Luxemburg norm the property ( β ) , nearly uniform convexity, the drop property and reflexivity are in pairs equivalent.

How to cite

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Kolwicz, Paweł. "The property ($\beta $) of Orlicz-Bochner sequence spaces." Commentationes Mathematicae Universitatis Carolinae 42.1 (2001): 119-132. <http://eudml.org/doc/248766>.

@article{Kolwicz2001,
abstract = {A characterization of property $(\beta )$ of an arbitrary Banach space is given. Next it is proved that the Orlicz-Bochner sequence space $l_\Phi (X)$ has the property $(\beta )$ if and only if both spaces $l_\Phi $ and $X$ have it also. In particular the Lebesgue-Bochner sequence space $l_p(X)$ has the property $(\beta )$ iff $X$ has the property $(\beta )$. As a corollary we also obtain a theorem proved directly in [5] which states that in Orlicz sequence spaces equipped with the Luxemburg norm the property $(\beta )$, nearly uniform convexity, the drop property and reflexivity are in pairs equivalent.},
author = {Kolwicz, Paweł},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Orlicz-Bochner space; property $(\beta )$; Orlicz space; property; Orlicz-Bochner sequence space; uniform convexity; nearly uniform convexity; drop property; Kadec-Klee property; reflexivity},
language = {eng},
number = {1},
pages = {119-132},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The property ($\beta $) of Orlicz-Bochner sequence spaces},
url = {http://eudml.org/doc/248766},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Kolwicz, Paweł
TI - The property ($\beta $) of Orlicz-Bochner sequence spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 1
SP - 119
EP - 132
AB - A characterization of property $(\beta )$ of an arbitrary Banach space is given. Next it is proved that the Orlicz-Bochner sequence space $l_\Phi (X)$ has the property $(\beta )$ if and only if both spaces $l_\Phi $ and $X$ have it also. In particular the Lebesgue-Bochner sequence space $l_p(X)$ has the property $(\beta )$ iff $X$ has the property $(\beta )$. As a corollary we also obtain a theorem proved directly in [5] which states that in Orlicz sequence spaces equipped with the Luxemburg norm the property $(\beta )$, nearly uniform convexity, the drop property and reflexivity are in pairs equivalent.
LA - eng
KW - Orlicz-Bochner space; property $(\beta )$; Orlicz space; property; Orlicz-Bochner sequence space; uniform convexity; nearly uniform convexity; drop property; Kadec-Klee property; reflexivity
UR - http://eudml.org/doc/248766
ER -

References

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