Inductive limit topologies on Orlicz spaces

Marian Nowak

Displaying similar documents to “Inductive limit topologies on Orlicz 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...

Copies of $l^{1}$ and $c_{o}$ in Musielak-Orlicz sequence spaces

Ghassan Alherk, Henryk Hudzik (1994)

Commentationes Mathematicae Universitatis Carolinae

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Criteria in order that a Musielak-Orlicz sequence space $l^{Φ}$ contains an isomorphic as well as an isomorphically isometric copy of $l^{1}$ are given. Moreover, it is proved that if $Φ = (Φ_{i})$ , where $Φ_{i}$ are defined on a Banach space, $X$ does not satisfy the $δ_{2}^{o}$ -condition, then the Musielak-Orlicz sequence space $l^{Φ} (X)$ of $X$ -valued sequences contains an almost isometric copy of $c_{o}$ . In the case of $X = I R$ it is proved also that if $l^{Φ}$ contains an isomorphic copy of $c_{o}$ , then $Φ$ does not satisfy the $δ_{2}^{o}$ -condition. These results...

Strongly exposed points in Musielak-Orlicz sequence spaces endowed with Orlicz norm

Zhongrui Shi, Chunyan Liu (2011)

Banach Center Publications

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A criterion for strongly exposed points of the unit ball $B (l_{M})$ in Musielak-Orlicz sequence spaces $l_{M}$ equipped with Orlicz norm is given.

Criteria for $k_{M} < \infty$ in Musielak-Orlicz spaces

Lianying Cao, Ting Fu Wang (2001)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, some necessary and sufficient conditions for $sup {k_{x} : ∥ x ∥^{0} = 1} < \infty$ in Musielak-Orlicz function spaces as well as in Musielak-Orlicz sequence spaces are given.

Intersections and algebraic sums of Musielak-Orlicz spaces

Hudzik, H. (1981)

Portugaliae mathematica

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Displaying similar documents to “Inductive limit topologies on Orlicz spaces”

Topological dual of non-locally convex Orlicz-Bochner spaces

Copies of l 1 and c o in Musielak-Orlicz sequence spaces

Strongly exposed points in Musielak-Orlicz sequence spaces endowed with Orlicz norm

Criteria for k M < ∞ in Musielak-Orlicz spaces

Intersections and algebraic sums of Musielak-Orlicz spaces

Copies of $l^{1}$ and $c_{o}$ in Musielak-Orlicz sequence spaces

Criteria for $k_{M} < \infty$ in Musielak-Orlicz spaces