On the reflexivity properties of Banach bundles and Banach modules
Abstract
In this paper, we investigate some reflexivity-type properties of separable measurable Banach bundles over a σ-finite measure space. Our two main results are the following:
• The fibers of a bundle are uniformly convex (with a common modulus of convexity) if and only if the space of its L p-sections is uniformly convex for every p ∈ (1,∞).
• The fibers of a bundle are reflexive if and only if the space of its L p-sections is reflexive for every p ∈ (1,∞). They generalise well-known results for Lebesgue–Bochner spaces.
Main Authors
Format
Articles
Research article
Published
2024
Series
Subjects
Publication in research information system
Publisher
Birkhäuser
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202401021018Use this for linking
Review status
Peer reviewed
ISSN
2662-2033
DOI
https://doi.org/10.1007/s43037-023-00315-9
Language
English
Published in
Banach Journal of Mathematical Analysis
Citation
- Lučić, M., Pasqualetto, E., & Vojnović, I. (2024). On the reflexivity properties of Banach bundles and Banach modules. Banach Journal of Mathematical Analysis, 18(1), Article 7. https://doi.org/10.1007/s43037-023-00315-9
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Additional information about funding
Open Access funding provided by University of Jyväskylä (JYU).
Copyright© The Author(s) 2023