Uniform convergence in the individual ergodic theorem for symmetric sequence spaces

2017/06/29 by Vladimir Chilin, Chilin, Vladimir, Azizhon Azizov +1
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1706.09860

arxiv created 2017/06/29 · openalex publication_date 2017/06/29 · arxiv updated 2017/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved that for any Dunford-Schwartz operator T acting in the space l_∞ and for each x∈ c₀ there exists an element \widehat x ∈ c₀ such that ‖ \frac 1n ∑_k=0^n-1T^k(x) - \widehat x ‖_∞ → 0.

Related

• Individual ergodic theorems for infinite measure
• Almost uniform convergence in noncommutative Dunford-Schwartz ergodic\n theorem
• Almost uniform and strong convergences in ergodic theorems for symmetric spaces
• Almost Uniform Convergence in Noncommutative Dunford-Schwartz Ergodic Theorem for p>1
• Counter-examples to the Dunford-Schwartz pointwise ergodic theorem on L¹+L^∞