| Title:
|
Copies of $l^1$ and $c_o$ in Musielak-Orlicz sequence spaces (English) |
| Author:
|
Alherk, Ghassan |
| Author:
|
Hudzik, Henryk |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1994 |
| Pages:
|
9-19 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Criteria in order that a Musielak-Orlicz sequence space $l^\Phi$ contains an isomorphic as well as an isomorphically isometric copy of $l^1$ are given. Moreover, it is proved that if $\Phi = (\Phi_i)$, where $\Phi_i$ are defined on a Banach space, $X$ does not satisfy the $\delta^o_2$-condition, then the Musielak-Orlicz sequence space $l^\Phi (X)$ of $X$-valued sequences contains an almost isometric copy of $c_o$. In the case of $X = I\!\!R$ it is proved also that if $l^\Phi$ contains an isomorphic copy of $c_o$, then $\Phi$ does not satisfy the $\delta^o_2$-condition. These results extend some results of [A] and [H2] to Musielak-Orlicz sequence spaces. (English) |
| Keyword:
|
Musielak-Orlicz sequence space |
| Keyword:
|
copy of $l^1$ |
| Keyword:
|
copy of $c_o$ |
| MSC:
|
46B20 |
| MSC:
|
46B25 |
| MSC:
|
46B45 |
| MSC:
|
46E30 |
| idZBL:
|
Zbl 0820.46013 |
| idMR:
|
MR1292578 |
| . |
| Date available:
|
2009-01-08T18:08:16Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118636 |
| . |
| Reference:
|
[A] Alherk G.: On the non-$l_n^{(1)}$ and locally uniformly non-$l_n^{(1)}$ properties and $l^1$ copies in Musielak-Orlicz space.Comment. Math. Univ. Carolinae 31 (1990), 435-443. MR 1078478 |
| Reference:
|
[AB] Aliprantis C.D., Burkinshaw O.: Positive operators.Pure and Applied Math., Academic Press, Inc., 1985. Zbl 1098.47001, MR 0809372 |
| Reference:
|
[BP] Bessaga C., Pełczyński A.: On bases and unconditional convergence of series in Banach spaces.Studia Math. 17 (1958), 151-164. MR 0115069 |
| Reference:
|
[DH] Denker M., Hudzik H.: Uniformly non-$l^{(1)}_n$ Musielak-Orlicz sequence spaces.Proc. Indian Acad. Sci. 101 (1991), 71-86. MR 1125480 |
| Reference:
|
[H1] Hudzik H.: On some equivalent conditions in Musielak-Orlicz spaces.Comment. Math. (Prace Matem.) 24 (1984), 57-64. Zbl 0564.46022, MR 0759055 |
| Reference:
|
[H2] Hudzik H.: Orlicz spaces containing a copy of $l^1$.Math. Japonica 34 (1989), 747-759. MR 1022152 |
| Reference:
|
[HY] Hudzik H., Ye Y.: Support functionals and smoothness in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm.Comment. Math. Univ. Carolinae 31 (1990), 661-684. Zbl 0721.46012, MR 1091364 |
| Reference:
|
[K] Kamińska A.: Flat Orlicz-Musielak sequence spaces.Bull. Acad. Polon. Sci. Math. 30 (1982), 347-352. MR 0707748 |
| Reference:
|
[KA] Kantorovich L.V., Akilov G.P.: Functional Analysis (in Russian).Nauka, Moscow, 1977. MR 0511615 |
| Reference:
|
[KR] Krasnoselskii M.A., Rutickii Ya.B.: Convex functions and Orlicz spaces.Groningen, 1961 (translation). |
| Reference:
|
[L] Luxemburg W.A.J.: Banach function spaces.Thesis, Delft, 1955. Zbl 0162.44701, MR 0072440 |
| Reference:
|
[M] Musielak J.: Orlicz spaces and modular spaces.Lecture Notes in Math. 1034, SpringerVerlag, 1983. Zbl 0557.46020, MR 0724434 |
| Reference:
|
[RR] Rao M.M., Ren Z.D.: Theory of Orlicz spaces.Pure and Applied Mathematics, Marcel Dekker, 1991. Zbl 0724.46032, MR 1113700 |
| Reference:
|
[T] Turett B.: Fenchel-Orlicz spaces.Dissertationes Math. 181 (1980), 1-60. Zbl 0435.46025, MR 0578390 |
| . |
