Abstract
AbstractIn this paper, we investigate some reflexivity-type properties of separable measurable Banach bundles over a $$\sigma $$
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 $$L^p$$
L
p
-sections is uniformly convex for every $$p\in (1,\infty )$$
p
∈
(
1
,
∞
)
.
The fibers of a bundle are reflexive if and only if the space of its $$L^p$$
L
p
-sections is reflexive for every $$p\in (1,\infty )$$
p
∈
(
1
,
∞
)
.
They generalise well-known results for Lebesgue–Bochner spaces.
Funder
Ministry of Science, Technological Development and Innovation of the Republic of Serbia
Bilateral project Austria-Serbia
International Balzan Prize Foundation
University of Jyväskylä
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference25 articles.
1. Aliprantis, C., Border, K.: Infinite Dimensional Analysis: A Hitchhiker’s Guide, Stud. Econ. Theory. Springer, Berlin (1999)
2. Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations, 1st edn. Universitext, Springer, Berlin (2011)
3. Day, M.M.: Uniform convexity in factor and conjugate spaces. Ann. Math. 2(45), 375–385 (1944)
4. Di Marino, S., Lučić, D., Pasqualetto, E.: Representation theorems for normed modules. Preprint, arXiv:2109.03509 (2021)
5. Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V.: Banach Space Theory, CMS Books Math./Ouvrages Math. SMC, Springer, New York (2011)
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