Let $L^{\varphi }\left(X\right)$ be an Orlicz-Bochner space defined by an Orlicz function $\varphi$ taking only finite values (not necessarily convex) over a $\sigma$-finite atomless measure space. It is proved that the topological dual $L^{\varphi }{\left(X\right)}^{*}$ of $L^{\varphi }\left(X\right)$ can be represented in the form: $L^{\varphi }{\left(X\right)}^{*}=L^{\varphi }{\left(X\right)}_n^{\sim }\oplus L^{\varphi }{\left(X\right)}_s^{\sim }$, where $L^{\varphi }{\left(X\right)}_n^{\sim }$ and $L^{\varphi }{\left(X\right)}_s^{\sim }$ denote the order continuous dual and the singular dual of $L^{\varphi }\left(X\right)$ respectively. The spaces $L^{\varphi }{\left(X\right)}^{*}$, $L^{\varphi }{\left(X\right)}_n^{\sim }$ and $L^{\varphi }{\left(X\right)}_s^{\sim }$ are examined by means of the H. Nakano’s theory of conjugate modulars. (Studia Mathematica 31 (1968), 439–449). The well known results of the...

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 $\Phi =\left({\Phi }_i\right)$, where ${\Phi }_i$ are defined on a Banach space, $X$ does not satisfy the ${\delta }_2^o$-condition, then the Musielak-Orlicz sequence space $l^{\Phi }\left(X\right)$ of $X$-valued sequences contains an almost isometric copy of $c_o$. In the case of $X=IR$ it is proved also that if $l^{\Phi }$ contains an isomorphic copy of $c_o$, then $\Phi$ does not satisfy the ${\delta }_2^o$-condition. These results...

A criterion for strongly exposed points of the unit ball $B\left(l_M\right)$ in Musielak-Orlicz sequence spaces $l_M$ equipped with Orlicz norm is given.