Displaying similar documents to “On the order-topological properties of the quotient space L / L A ”

Order continuous seminorms and weak compactness in Orlicz spaces.

Marian Nowak (1993)

Collectanea Mathematica

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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...

Topological dual of non-locally convex Orlicz-Bochner spaces

Marian Nowak (1999)

Commentationes Mathematicae Universitatis Carolinae

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Let L ϕ ( X ) be an Orlicz-Bochner space defined by an Orlicz function ϕ taking only finite values (not necessarily convex) over a σ -finite atomless measure space. It is proved that the topological dual L ϕ ( X ) * of L ϕ ( X ) can be represented in the form: L ϕ ( X ) * = L ϕ ( X ) n ∼ ⊕ L ϕ ( X ) s ∼ , where L ϕ ( X ) n ∼ and L ϕ ( X ) s ∼ denote the order continuous dual and the singular dual of L ϕ ( X ) respectively. The spaces L ϕ ( X ) * , L ϕ ( X ) n ∼ and L ϕ ( X ) 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...

On the locally uniformly weak star rotundity of Orlicz spaces.

Ting Fu Wang, Zhong Rui Shi (1994)

Revista Matemática de la Universidad Complutense de Madrid

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In the paper, a sufficient and necessary condition is given for the locally uniformly weak star rotundity of Orlicz spaces with Orlicz norms.