2024/06/12 by Maciej Ciesielski, Ciesielski, Maciej, Grzegorz Lewicki +1
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2406.08095
openalex publication_date 2024/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
First, we solve a crucial problem under which conditions increasing uniform K-monotonicity is equivalent to lower locally uniform K-monotonicity. Next, we investigate properties of substochastic operators on L1+L^∞ with applications. Namely, we show that a countable infinite combination of substochastic operators is also substochastic. Using K-monotonicity properties, we prove several theorems devoted to the convergence of the sequence of substochastic operators in the norm of a symmetric space E under addition assumption on E. In our final discussion we focus on compactness of admissible operators for arbitrary Banach couples.