On compactness in L⁰-modules

2017/11/27 by Asgar Jamneshan, Jamneshan, Asgar, José Miguel Zapata +1
Mathematics · #03C90 #46H25 #54D30 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.1711.09785

openalex publication_date 2017/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Several results in functional analysis are extended to the setting of L⁰-modules, where L⁰ denotes the ring of all measurable functions x\colon Ω→ ℝ. The focus is on results involving compactness. To this end, a notion of stable compactness is introduced, and it is argued that the conventional notion of compactness does not allow to establish a functional analytic discourse in L⁰-modules. Several characterizations of stable compactness are discussed, and its importance in applications is highlighted.

Citations

• Vector duality via conditional extension of dual pairs

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