A note on copies of in spaces of weak* measurable functions
Commentationes Mathematicae Universitatis Carolinae (2000)
- Volume: 41, Issue: 4, page 761-764
- ISSN: 0010-2628
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topFerrando, Juan Carlos. "A note on copies of $c_0$ in spaces of weak* measurable functions." Commentationes Mathematicae Universitatis Carolinae 41.4 (2000): 761-764. <http://eudml.org/doc/248590>.
@article{Ferrando2000,
abstract = {If $(\Omega ,\Sigma ,\mu )$ is a finite measure space and $X$ a Banach space, in this note we show that $L_\{w^\{\ast \}\}^\{1\}(\mu ,X^\{\ast \})$, the Banach space of all classes of weak* equivalent $X^\{\ast \}$-valued weak* measurable functions $f$ defined on $\Omega $ such that $\Vert f(\omega )\Vert \le g(\omega )$ a.e. for some $g\in L_\{1\}(\mu )$ equipped with its usual norm, contains a copy of $c_\{0\}$ if and only if $X^\{\ast \}$ contains a copy of $c_\{0\}$.},
author = {Ferrando, Juan Carlos},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {weak* measurable function; copy of $c_0$; copy of $\ell _1$; weak measurable function; copy of ; copy of },
language = {eng},
number = {4},
pages = {761-764},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on copies of $c_0$ in spaces of weak* measurable functions},
url = {http://eudml.org/doc/248590},
volume = {41},
year = {2000},
}
TY - JOUR
AU - Ferrando, Juan Carlos
TI - A note on copies of $c_0$ in spaces of weak* measurable functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 4
SP - 761
EP - 764
AB - If $(\Omega ,\Sigma ,\mu )$ is a finite measure space and $X$ a Banach space, in this note we show that $L_{w^{\ast }}^{1}(\mu ,X^{\ast })$, the Banach space of all classes of weak* equivalent $X^{\ast }$-valued weak* measurable functions $f$ defined on $\Omega $ such that $\Vert f(\omega )\Vert \le g(\omega )$ a.e. for some $g\in L_{1}(\mu )$ equipped with its usual norm, contains a copy of $c_{0}$ if and only if $X^{\ast }$ contains a copy of $c_{0}$.
LA - eng
KW - weak* measurable function; copy of $c_0$; copy of $\ell _1$; weak measurable function; copy of ; copy of
UR - http://eudml.org/doc/248590
ER -
References
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