| Title:
|
A note on copies of $c_0$ in spaces of weak* measurable functions (English) |
| Author:
|
Ferrando, J. C. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
761-764 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\|f(\omega )\| \leq g(\omega )$ 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 $c_{0}$. (English) |
| Keyword:
|
weak* measurable function |
| Keyword:
|
copy of $c_0$ |
| Keyword:
|
copy of $\ell_1$ |
| MSC:
|
46B20 |
| MSC:
|
46E40 |
| MSC:
|
46G10 |
| idZBL:
|
Zbl 1050.46512 |
| idMR:
|
MR1800168 |
| . |
| Date available:
|
2009-01-08T19:07:03Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119207 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Diestel J.: Sequences and Series in Banach Spaces.GTM 92, Springer-Verlag, 1984. MR 0737004 |
| Reference:
|
[4] Dunford N., Schwartz J.T.: Linear Operators. Part I.John Wiley, Wiley Interscience, New York, 1988. Zbl 0635.47001, MR 1009162 |
| Reference:
|
[5] Hoffmann-Jørgensen J.: Sums of independent Banach space valued random variables.Studia Math. 52 (1974), 159-186. MR 0356155 |
| Reference:
|
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| Reference:
|
[7] Kwapień S.: On Banach spaces containing $c_{0}$.Studia Math. 52 (1974), 187-188. MR 0356156 |
| Reference:
|
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| Reference:
|
[9] Saab E., Saab P.: A stability property of a class of Banach spaces not containing a complemented copy of $\ell_{1}$.Proc. Amer. Math. Soc. 84 (1982), 44-46. MR 0633274 |
| . |
