Topological dual of non-locally convex Orlicz-Bochner spaces

Marian Nowak

Displaying similar documents to “Topological dual of non-locally convex Orlicz-Bochner spaces”

Inductive limit topologies on Orlicz spaces

Marian Nowak (1991)

Commentationes Mathematicae Universitatis Carolinae

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Let $L^{ϕ}$ be an Orlicz space defined by a convex Orlicz function $ϕ$ and let $E^{ϕ}$ be the space of finite elements in $L^{ϕ}$ (= the ideal of all elements of order continuous norm). We show that the usual norm topology $𝒯_{ϕ}$ on $L^{ϕ}$ restricted to $E^{ϕ}$ can be obtained as an inductive limit topology with respect to some family of other Orlicz spaces. As an application we obtain a characterization of continuity of linear operators defined on $E^{ϕ}$ .

Order continuous linear functionals on non-locally convex Orlicz spaces

Marian Nowak (1992)

Commentationes Mathematicae Universitatis Carolinae

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The space of all order continuous linear functionals on an Orlicz space $L^{ϕ}$ defined by an arbitrary (not necessarily convex) Orlicz function $ϕ$ is described.

Weak uniform rotundity of Musielak--Orlicz spaces

Małgorzata Doman (1991)

Commentationes Mathematicae Universitatis Carolinae

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We give necessary and sufficient conditions for weak uniform rotundity of Musielak–Orlicz spaces $L_{ϕ}$ with the Luxemburg norm. The result is a generalization of a theorem by Kami’nska and Kurc.