Geodesic
On vector valued measure spaces of bounded $\Phi$-variation containing copies of $\ell_\infty$
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 1, pp. 67-72 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 46B20, 46E40 
@article{CMJ_2001_51_1_a6,
     author = {Rivera, Mar{\'\i}a J.},
     title = {On vector valued measure spaces of bounded $\Phi$-variation containing copies of $\ell_\infty$},
     journal = {Czechoslovak Mathematical Journal},
     pages = {67--72},
     year = {2001},
     volume = {51},
     number = {1},
     mrnumber = {1814633},
     zbl = {1079.46513},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2001_51_1_a6/}
}
TY  - JOUR
AU  - Rivera, María J.
TI  - On vector valued measure spaces of bounded $\Phi$-variation containing copies of $\ell_\infty$
JO  - Czechoslovak Mathematical Journal
PY  - 2001
SP  - 67
EP  - 72
VL  - 51
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2001_51_1_a6/
LA  - en
ID  - CMJ_2001_51_1_a6
ER  - 
%0 Journal Article
%A Rivera, María J.
%T On vector valued measure spaces of bounded $\Phi$-variation containing copies of $\ell_\infty$
%J Czechoslovak Mathematical Journal
%D 2001
%P 67-72
%V 51
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2001_51_1_a6/
%G en
%F CMJ_2001_51_1_a6
Rivera, María J. On vector valued measure spaces of bounded $\Phi$-variation containing copies of $\ell_\infty$. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 1, pp. 67-72. http://geodesic.mathdoc.fr/item/CMJ_2001_51_1_a6/

[1] Ch. J. de la Vallée Poussin: Sur l’integrale de Lebesgue. Trans. Amer. Math. Soc. 16 (1915), 435–501. | DOI | MR

[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

[3] G. Emmanuelle: On complemented copies of $c_0$ in $L_{X}^{p}$, $1 \le p < \infty $. Proc. Amer. Math. Soc. 104, 785–786.

[4] J. C. Ferrando: Copies of $c_0$ in certain vector-valued function Banach spaces. Math. Scand. 77 (1995), 148–152. | DOI | MR

[5] J. Mendoza: Copies of $\ell _{\infty }$ in $L^{p} (\mu ;X)$. Proc. Amer. Math. Soc. 109 (1990), 125–127. | MR

[6] M. M. Rao and Z. D. Ren: Theory of Orlicz Spaces. Marcel Dekker Inc., 1991. | MR

[7] H. P. Rosenthal: On relatively disjoint families of measures with some applications to Banach spaces theory. Studia Math. 37 (1970), 13–16. | DOI | MR

[8] J. J. Uhl Jr.: Orlicz spaces of finitely additive set functions. Studia Math. XXIX (1967), 19–58. | MR | Zbl