2024/10/20 by Javier Falcó, Falco, Javier, Daniel Isert +1
Computer Science · Engineering · #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.2410.15459
openalex publication_date 2024/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the reflexivity and strong subdifferentiability within the framework of group invariant mappings. We show that a Banach space is G-reflexive if the norm of its dual is G-strong subdifferentiable. To do this, we extend numerous classical concepts in functional analysis such as weak and weak-star topologies, the polar of a set, duality mapping, to the framework of group invariant mappings. We also extend many classical results in functional analysis including Banach-Alaoglu-Bourbaki's theorem, James' theorem, Moreau's maximum formula, and Krein-Smulian's theorem, to this context. To conclude, we provide an application of these new results by providing sufficient conditions to ensure the existence of closed Banach spaces inside the set of norm-attaining functionals of a Banach space.