Integration in Orlicz-Bochner Spaces

Integration in Orlicz-Bochner Spaces

Let (Ω,Σ,μ) be a complete σ-finite measure space, φ be a Young function, and X and Y be Banach spaces. Let Lφ(X) denote the Orlicz-Bochner space, and Tφ∧ denote the finest Lebesgue topology on Lφ(X). We study the problem of integral representation of (Tφ∧,·Y)-continuous linear operators T:Lφ(X)→Y wi...

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Main Author: Marian Nowak
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2018/9380350
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spelling doaj-11f996522b654e5a8986a03242b338c52020-11-24T21:00:25ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/93803509380350Integration in Orlicz-Bochner SpacesMarian Nowak0Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Ul. Szafrana 4A, 65–516 Zielona Góra, PolandLet (Ω,Σ,μ) be a complete σ-finite measure space, φ be a Young function, and X and Y be Banach spaces. Let Lφ(X) denote the Orlicz-Bochner space, and Tφ∧ denote the finest Lebesgue topology on Lφ(X). We study the problem of integral representation of (Tφ∧,·Y)-continuous linear operators T:Lφ(X)→Y with respect to the representing operator-valued measures. The relationships between (Tφ∧,·Y)-continuous linear operators T:Lφ(X)→Y and the topological properties of their representing operator measures are established.http://dx.doi.org/10.1155/2018/9380350
collection DOAJ
language English
format Article
sources DOAJ
author Marian Nowak
spellingShingle Marian Nowak
Integration in Orlicz-Bochner Spaces
Journal of Function Spaces
author_facet Marian Nowak
author_sort Marian Nowak
title Integration in Orlicz-Bochner Spaces
title_short Integration in Orlicz-Bochner Spaces
title_full Integration in Orlicz-Bochner Spaces
title_fullStr Integration in Orlicz-Bochner Spaces
title_full_unstemmed Integration in Orlicz-Bochner Spaces
title_sort integration in orlicz-bochner spaces
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2018-01-01
description Let (Ω,Σ,μ) be a complete σ-finite measure space, φ be a Young function, and X and Y be Banach spaces. Let Lφ(X) denote the Orlicz-Bochner space, and Tφ∧ denote the finest Lebesgue topology on Lφ(X). We study the problem of integral representation of (Tφ∧,·Y)-continuous linear operators T:Lφ(X)→Y with respect to the representing operator-valued measures. The relationships between (Tφ∧,·Y)-continuous linear operators T:Lφ(X)→Y and the topological properties of their representing operator measures are established.
url http://dx.doi.org/10.1155/2018/9380350
work_keys_str_mv AT mariannowak integrationinorliczbochnerspaces
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