Testing compactness of linear operators

2024/11/26 by Timo S. Hänninen, Hänninen, Timo S., Tuomas Oikari +1
Computer Science · Engineering · #Advanced Control Systems Optimization #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.2411.17654

openalex publication_date 2024/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

Let (F_i) be a sequence of sets in a Banach space X. For what sequences does the condition \limsup_{i→ ∞} sup_{fi∈ Fi} ‖Tf_i‖_Y=0 hold for every Banach space Y and every compact operator T:X→ Y? We answer this question by giving sufficient (and necessary) criteria for such sequences. We illustrate the applicability of the criteria by examples from literature and by characterizing the L^p→ L^p compactness of dyadic paraproducts on general measure spaces.

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