Order continuous seminorms and weak compactness in Orlicz spaces.

Nowak, Marian. "Order continuous seminorms and weak compactness in Orlicz spaces.." Collectanea Mathematica 44.1-2-3 (1993): 217-236. <http://eudml.org/doc/42109>.

@article{Nowak1993,
abstract = {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.},
author = {Nowak, Marian},
journal = {Collectanea Mathematica},
keywords = {Espacio de Orlicz; Seminormas; Compacidad; Espacios de Riesz; Orlicz space; Young function; complementary function in the sense of Young; Mackey topology; order continuous (= absolutely continuous) Riesz semi-norms},
language = {eng},
number = {1-2-3},
pages = {217-236},
title = {Order continuous seminorms and weak compactness in Orlicz spaces.},
url = {http://eudml.org/doc/42109},
volume = {44},
year = {1993},
}

TY - JOUR
AU - Nowak, Marian
TI - Order continuous seminorms and weak compactness in Orlicz spaces.
JO - Collectanea Mathematica
PY - 1993
VL - 44
IS - 1-2-3
SP - 217
EP - 236
AB - 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.
LA - eng
KW - Espacio de Orlicz; Seminormas; Compacidad; Espacios de Riesz; Orlicz space; Young function; complementary function in the sense of Young; Mackey topology; order continuous (= absolutely continuous) Riesz semi-norms
UR - http://eudml.org/doc/42109
ER -