Abstract: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 $X = \Bbb R$ 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.
Keywords: Musielak-Orlicz sequence space, copy of $l^1$, copy of $c_o$
AMS Subject Classification: 46B20, 46B25, 46E30