Let L-phi be an Orlicz space defined by a Young function phi over a sigma-finite measure space, and let phi* denote the complementary function in the sense of Young. We give a characterization of the Mackey topology tau(L*,L-phi*) in terms of some family of norms defined by some regular Young functions. Next we describe order continuous (=absolutely continuous) Riesz seminorms on L-phi, and obtain a criterion for relative sigma(L-phi,L-phi*)-compactness in L-phi. As an application we get a representation of L-phi as the union of some family of other Orlicz spaces. Finally, we apply the above results to the theory of Lebesgue spaces.
@article{urn:eudml:doc:42109,
title = {Order continuous seminorms and weak compactness in Orlicz spaces.},
journal = {Collectanea Mathematica},
volume = {44},
year = {1993},
pages = {217-236},
zbl = {0815.46027},
mrnumber = {MR1280740},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42109}
}
Nowak, Marian. Order continuous seminorms and weak compactness in Orlicz spaces.. Collectanea Mathematica, Tome 44 (1993) pp. 217-236. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42109/