| Title:
|
Embedding $c_0$ in ${\rm bvca}(\Sigma,X)$ (English) |
| Author:
|
Ferrando, J. C. |
| Author:
|
Ruiz, L. M. Sánchez |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
679-688 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
If $(\Omega ,\Sigma ) $ is a measurable space and $X$ a Banach space, we provide sufficient conditions on $\Sigma $ and $X$ in order to guarantee that $\mathop {\mathrm bvca}( \Sigma ,X) $, the Banach space of all $X$-valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of $c_{0}$ if and only if $X$ does. (English) |
| Keyword:
|
countably additive vector measure of bounded variation |
| Keyword:
|
Pettis integrable function space |
| Keyword:
|
copy of $c_{0}$ |
| Keyword:
|
copy of $\ell _{\infty }$ |
| MSC:
|
28A33 |
| MSC:
|
28B05 |
| MSC:
|
46B25 |
| MSC:
|
46E27 |
| MSC:
|
46G10 |
| idZBL:
|
Zbl 1174.46016 |
| idMR:
|
MR2337622 |
| . |
| Date available:
|
2009-09-24T11:48:28Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128197 |
| . |
| Reference:
|
[1] J. Bourgain: An averaging result for $c_{0}$-sequences.Bull. Soc. Math. Belg., Sér. B 30 (1978), 83–87. Zbl 0417.46019, MR 0549653 |
| Reference:
|
[2] P. Cembranos, J. Mendoza: Banach Spaces of Vector-Valued Functions. Lecture Notes in Mathematics Vol. 1676.Springer-Verlag, Berlin, 1997. MR 1489231 |
| Reference:
|
[3] J. Diestel: Sequences and Series in Banach Spaces.Graduate Texts in Mathematics, 92, Springer-Verlag, New York-Heidelberg-Berlin, 1984. MR 0737004 |
| Reference:
|
[4] J. Diestel, J. Uhl: Vector Measures. Mathematical Surveys, No 15.Am. Math. Soc., Providence, 1977. MR 0453964 |
| Reference:
|
[5] L. Drewnowski: When does $\mathop {\mathrm ca}( \Sigma ,Y) $ contain a copy of $\ell _{\infty }$ or $c_{0}$.Proc. Am. Math. Soc. 109 (1990), 747–752. MR 1012927, 10.1090/S0002-9939-1990-1012927-4 |
| Reference:
|
[6] J. C. Ferrando: When does $( \Sigma ,X)$ contain a copy of $\ell _{\infty }$.Math. Scand. 74 (1994), 271–274. MR 1298368, 10.7146/math.scand.a-12496 |
| Reference:
|
[7] P. Habala, P. Hájek, and V. Zizler: Introduction to Banach Space.Matfyzpress, Prague, 1996. |
| Reference:
|
[8] E. Hewitt, K. Stromberg: Real and Abstract Analysis. Graduate Texts in Mathematics 25.Springer-Verlag, New York-Heidelberg-Berlin, 1975. MR 0367121 |
| Reference:
|
[9] K. Musial: The weak Radon-Nikodým property in Banach spaces.Stud. Math. 64 (1979), 151–173. Zbl 0405.46015, MR 0537118, 10.4064/sm-64-2-151-174 |
| Reference:
|
[10] E. Saab, P. Saab: On complemented copies of $c_{0} $ in injective tensor products.Contemp. Math. 52 (1986), 131–135. 10.1090/conm/052/840704 |
| Reference:
|
[11] M. Talagrand: Quand l’espace des mesures a variation bornée est-it faiblement sequentiellement complet.Proc. Am. Math. Soc. 90 (1984), 285–288. (French) MR 0727251 |
| . |
