Uniformly $\mu $-continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces

Krzysztof Feledziak

Displaying similar documents to “Uniformly $μ$ -continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces”

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: $L^{ϕ} {(X)}^{*} = L^{ϕ} {(X)}_{n}^{\sim} \oplus L^{ϕ} {(X)}_{s}^{\sim}$ , where $L^{ϕ} {(X)}_{n}^{\sim}$ and $L^{ϕ} {(X)}_{s}^{\sim}$ denote the order continuous dual and the singular dual of $L^{ϕ} (X)$ respectively. The spaces $L^{ϕ} {(X)}^{*}$ , $L^{ϕ} {(X)}_{n}^{\sim}$ and $L^{ϕ} {(X)}_{s}^{\sim}$ 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...

Orlicz-Pettis topologies in function spaces.

Ch. Swartz (1979)

Publications de l'Institut Mathématique [Elektronische Ressource]

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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 $E^{ϕ}$ .

Displaying similar documents to “Uniformly μ -continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces”

Topological dual of non-locally convex Orlicz-Bochner spaces

Orlicz-Pettis topologies in function spaces.

Inductive limit topologies on Orlicz spaces

Displaying similar documents to “Uniformly $μ$ -continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces”