Order continuous seminorms and weak compactness in Orlicz spaces

• Autores: Marian Nowak
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 44, Fasc. 1-3, 1993, págs. 217-236
• Idioma: inglés
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• Resumen

  • Let $L^\varphi$ be an Orlicz space defined by a Young function $\varphi$ over a $\sigma$-finite measure space, and let $\varphi^\ast$ denote the complementary function in the sense of Young. We give a characterization of the Mackey topology $\tau (L^\ast, L^{\varphi^\ast} )$ in terms of some family of norms defined by some regular Young functions. Next, we describe order continuous (= absolutely continuous) Riesz seminorms on $L^\varphi$, and obtain a criterion for relative $\sigma(L^\varphi, L^{\varphi^\ast} )$-compactness in $L^\varphi$. As an application we get a representation of $L^\varphi$ as the union of some family of other Orlicz spaces. Finally, we apply the above results to the theory of Lebesgue spaces.