Let $L^\varphi (X)$ 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 $L^\varphi (X)^*$ of $L^\varphi (X)$ can be represented in the form: $L^\varphi (X)^*=L^\varphi (X)^\sim _n\oplus L^\varphi (X)^\sim _s$, where $L^\varphi (X)^\sim_n$ and $L^\varphi (X)^\sim_s$ denote the order continuous dual and the singular dual of $L^\varphi (X)$ respectively. The spaces $L^\varphi (X)^*$, $L^\varphi (X)^\sim _n$ and $L^\varphi (X)^\sim _s$ 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 duality theory of Orlicz spaces are extended to the vector-valued setting.
@article{119107,
author = {Marian Nowak},
title = {Topological dual of non-locally convex Orlicz-Bochner spaces},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {40},
year = {1999},
pages = {511-529},
zbl = {1010.46028},
mrnumber = {1732484},
language = {en},
url = {http://dml.mathdoc.fr/item/119107}
}
Nowak, Marian. Topological dual of non-locally convex Orlicz-Bochner spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 511-529. http://gdmltest.u-ga.fr/item/119107/
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