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

作者：Mitrea Dorina; Mitrea Irina^*; Mitrea Marius; Ziade Elia

来源：Journal of Functional Analysis, 2012, 262(11): 4766-4830.

DOI：10.1016/j.jfa.2012.03.012

• Semigroupoid
• Metrization theorem
• Quasi-metric space
• Completeness
• Separability
• Pointwise convergence
• Boolean algebra
• Capacity
• Quasi-Banach function space
• Fatou property

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.

• 出版日期2012-6-1