Ergodicity and super weak compactness

2023/02/11 by Guillaume Grelier, M. Raja, Grelier, Guillaume +1
Computer Science · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2302.05656

openalex publication_date 2023/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a closed convex subset of a Banach space is (super-)weakly compact if and only if it is (super)-ergodic. As a consequence we deduce that super weakly compact sets are characterized by the fixed point property for continuous affine mappings. We also prove that the M-(fixed point property for affine isometries) implies the Banach-Saks property.

Related

• Nonlinear aspects of super weakly compact sets
• Applications of the quantification of super weak compactness
• Grothendieck's compactness principle for the absolute weak topology
• Weak Compactness and Fixed Point Property for Affine Bi-Lipschitz Maps
• One side James' Compactness Theorem