Nonatomic submeasures on \mathbb N and the Banach space ℓ₁

2021/06/15 by Lech Drewnowski, Drewnowski, Lech
Mathematics · #11B05 #28A12 #46A45 #46B03 #46B25 #46B45 #47L05 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #advanced mathematical theories #math.FA #msc:11B05 #msc:28A12 #msc:46A45 #msc:46B03 #msc:46B25 #msc:46B45 #msc:47L05

paper · pdf · doi:10.48550/arxiv.2106.08196

6 pages

arxiv created 2021/06/15 · openalex publication_date 2021/06/15 · arxiv updated 2021/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Nonatomic bounded sequences in ℓ₁, that is, those giving rise to nonatomic submeasures on \mathbb N are introduced and shown to form a closed subspace nonat(ℓ₁) of ℓ_∞(ℓ₁), and some spaces of relevant operators in ℓ₁ are considered.

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