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Keywords:
Musielak-Orlicz sequence space; copy of $l^1$; copy of $c_o$
Musielak-Orlicz sequence space; copy of $l^1$; copy of $c_o$
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.
References:
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