Banach Journal of Mathematical Analysis

Approximative compactness in Musielak–Orlicz function spaces of Bochner type

Shaoqiang Shang and Yunan Cui

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Abstract

In this article, we give the criteria for approximative compactness of every proximinal convex subset of Musielak–Orlicz–Bochner function spaces equipped with the Orlicz norm. As a corollary, we give the criteria for approximative compactness of Musielak–Orlicz–Bochner function spaces equipped with the Orlicz norm.

Article information

Source
Banach J. Math. Anal., Volume 11, Number 1 (2017), 143-163.

Dates
Received: 21 October 2015
Accepted: 27 February 2016
First available in Project Euclid: 30 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1480474817

Digital Object Identifier
doi:10.1215/17358787-3773029

Mathematical Reviews number (MathSciNet)
MR3577373

Zentralblatt MATH identifier
1383.46030

Subjects
Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords
approximative compactness Radon–Nikodym property Musielak–Orlicz–Bochner function space Orlicz norm

Citation

Shang, Shaoqiang; Cui, Yunan. Approximative compactness in Musielak–Orlicz function spaces of Bochner type. Banach J. Math. Anal. 11 (2017), no. 1, 143--163. doi:10.1215/17358787-3773029. https://projecteuclid.org/euclid.bjma/1480474817


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References

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