| Title:
|
On vector valued measure spaces of bounded $\Phi$-variation containing copies of $\ell_\infty$ (English) |
| Author:
|
Rivera, María J. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
67-72 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Given a Young function $\Phi $, we study the existence of copies of $c_0$ and $\ell _{\infty }$ in $\mathop {\mathrm cabv}\nolimits _{\Phi } (\mu ,X)$ and in $\mathop {\mathrm cabsv}\nolimits _{\Phi } (\mu ,X)$, the countably additive, $\mu $-continuous, and $X$-valued measure spaces of bounded $\Phi $-variation and bounded $\Phi $-semivariation, respectively. (English) |
| MSC:
|
46B20 |
| MSC:
|
46E40 |
| idZBL:
|
Zbl 1079.46513 |
| idMR:
|
MR1814633 |
| . |
| Date available:
|
2009-09-24T10:39:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127627 |
| . |
| Reference:
|
[1] Ch. J. de la Vallée Poussin: Sur l’integrale de Lebesgue.Trans. Amer. Math. Soc. 16 (1915), 435–501. MR 1501024, 10.2307/1988879 |
| Reference:
|
[2] L. Drewnowski and G. Emmanuelle: The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of $c_0$.Studia Math. 104 (1993), 110–123. MR 1211812 |
| Reference:
|
[3] G. Emmanuelle: On complemented copies of $c_0$ in $L_{X}^{p}$, $1 \le p < \infty $.Proc. Amer. Math. Soc. 104, 785–786. |
| Reference:
|
[4] J. C. Ferrando: Copies of $c_0$ in certain vector-valued function Banach spaces.Math. Scand. 77 (1995), 148–152. MR 1365911, 10.7146/math.scand.a-12555 |
| Reference:
|
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| Reference:
|
[6] M. M. Rao and Z. D. Ren: Theory of Orlicz Spaces.Marcel Dekker Inc., 1991. MR 1113700 |
| Reference:
|
[7] H. P. Rosenthal: On relatively disjoint families of measures with some applications to Banach spaces theory.Studia Math. 37 (1970), 13–16. MR 0270122, 10.4064/sm-37-1-13-36 |
| Reference:
|
[8] J. J. Uhl Jr.: Orlicz spaces of finitely additive set functions.Studia Math. XXIX (1967), 19–58. Zbl 0158.13703, MR 0226395 |
| . |
