# Order continuous seminorms and weak compactness in Orlicz spaces.

Collectanea Mathematica (1993)

- Volume: 44, Issue: 1-2-3, page 217-236
- ISSN: 0010-0757

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topNowak, 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 -

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