Collective order convergence and collectively qualified sets of operators

2024/08/07 by Eduard Emelyanov, Emelyanov, Eduard · 3 citations
Computer Science · #46A40 #46B42 #47B60 #Distributed Control Multi-Agent Systems #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2408.03671

openalex publication_date 2024/08/07 · openalex created_date 2024/10/27 · openalex updated_date 2026/07/28

Abstract

Collective versions of order convergences and corresponding types of collectively qualified sets of operators in vector lattices are investigated. It is proved that collectively order to norm bounded sets are bounded in the operator norm and collectively order continuous sets are collectively order bounded.

Cited by

• Equi-bounded on order intervals families of semi-norms
• On Levi operators between normed and vector lattices
• Automatic boundedness of some operators between ordered and topological vector spaces

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