Geodesic
Copies of $l^1$ and $c_o$ in Musielak-Orlicz sequence spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 1, pp. 9-19 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 46B20, 46B25, 46B45, 46E30
Keywords: Musielak-Orlicz sequence space; copy of $l^1$; copy of $c_o$ 
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     title = {Copies of $l^1$ and $c_o$ in {Musielak-Orlicz} sequence spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
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     year = {1994},
     volume = {35},
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Alherk, Ghassan; Hudzik, Henryk. Copies of $l^1$ and $c_o$ in Musielak-Orlicz sequence spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 1, pp. 9-19. http://geodesic.mathdoc.fr/item/CMUC_1994_35_1_a1/