Abstract capacitary estimates and the completeness and separability of certain classes of non-locally convex topological vector spaces

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• 作者：Dorina Mitrea^a ; ¹ ; ^{mitread@missouri.edu} ; Irina Mitrea^b ; ² ; ^{imitrea@temple.edu} ; Marius Mitrea^a ; ^{mitream@missouri.edu} ; Elia Ziadé ; ^a ; ^{etzm7f@mail.missouri.edu}
• 关键词：Semigroupoid ; Metrization theorem ; Quasi-metric space ; Completeness ; Separability ; Pointwise convergence ; Boolean algebra ; Capacity ; Quasi-Banach function space ; Fatou property
• 刊名：Journal of Functional Analysis
• 出版年：2012
• 期刊代码：75_00221236
• 类别：mt
• 出版时间：1 June, 2012
• 卷：262
• 期：11
• 页码：4766-4830
• 文件大小：437 K

摘要

We are concerned with establishing completeness and separability criteria for large classes of topological vector spaces which are typically non-locally convex, including Lebesgue-like spaces, Lorentz spaces, Orlicz spaces, mixed-normed spaces, tent spaces, and discrete Triebel-Lizorkin and Besov spaces. For vector spaces of measurable functions we also derive pointwise convergence results. Our approach relies on abstract capacitary estimates and works in certain cases of interest even in the absence of a background measure space and/or of a vector space structure.