| Title:
|
On Pettis integrability (English) |
| Author:
|
Ferrando, J. C. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
1009-1015 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Assuming that $(\Omega , \Sigma , \mu )$ is a complete probability space and $X$ a Banach space, in this paper we investigate the problem of the $X$-inheritance of certain copies of $c_0$ or $\ell _{\infty }$ in the linear space of all [classes of] $X$-valued $\mu $-weakly measurable Pettis integrable functions equipped with the usual semivariation norm. (English) |
| Keyword:
|
Pettis integrable function space |
| Keyword:
|
copy of $c_0$ |
| Keyword:
|
copy of $\ell _{\infty }$ |
| Keyword:
|
countably additive vector measure |
| Keyword:
|
WRNP |
| Keyword:
|
CRP |
| MSC:
|
28B05 |
| MSC:
|
46G10 |
| idZBL:
|
Zbl 1080.46515 |
| idMR:
|
MR2018846 |
| . |
| Date available:
|
2009-09-24T11:08:42Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127856 |
| . |
| Reference:
|
[1] P. Cembranos and J. Mendoza: Banach Spaces of Vector-Valued Functions. Lecture Notes in Math. 1676.Springer, 1997. MR 1489231 |
| Reference:
|
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| Reference:
|
[3] J. Diestel and J. Uhl: Vector Measures. Math Surveys 15.Amer. Math. Soc. Providence, 1977. MR 0453964 |
| Reference:
|
[4] L. Drewnowski: Copies of $\ell _{\infty }$ in an operator space.Math. Proc. Camb. Phil. Soc. 108 (1990), 523–526. MR 1068453, 10.1017/S0305004100069401 |
| Reference:
|
[5] L. Drewnowski, M. Florencio and P. J. Paúl: The space of Pettis integrable functions is barrelled.Proc. Amer. Math. Soc. 114 (1992), 687–694. MR 1107271, 10.1090/S0002-9939-1992-1107271-2 |
| Reference:
|
[6] D. van Dulst: Characterizations of Banach Spaces not containing $\ell _{1}$. CWI Tract.Amsterdam, 1989. MR 1002733 |
| Reference:
|
[7] J. C. Ferrando: On sums of Pettis integrable random elements.Quaestiones Math. 25 (2002), 311–316. Zbl 1036.46010, MR 1931282, 10.2989/16073600209486018 |
| Reference:
|
[8] F. J. Freniche: Embedding $c_0$ in the space of Pettis integrable functions.Quaestiones Math. 21 (1998), 261–267. Zbl 0963.46025, MR 1701785, 10.1080/16073606.1998.9632045 |
| Reference:
|
[9] E. Hewitt and K. Stromberg: Real and Abstract Analysis. GTM 25.Springer Verlag, 1965. MR 0367121 |
| Reference:
|
[10] K. Musial: The weak Radon-Nikodým property in Banach spaces.Studia Math. 64 (1979), 151–173. Zbl 0405.46015, MR 0537118, 10.4064/sm-64-2-151-174 |
| . |
