The Krengel's theorem for compact operators between locally solid vector lattices

2022/01/28 by Omid Zabeti, Zabeti, Omid
Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2201.12429

openalex publication_date 2022/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose X is a locally solid vector lattice. It is known that there are several non-equivalent notions for compact operators on X. Furthermore, notion of the AM-property in X as an extension for the AM-spaces in Banach lattices has been considered, recently. In this paper, we establish a variant of the known Krengel's theorem for different types of compact operators between locally solid vector lattices.

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