On KB and Levi operators in Banach lattices

2023/12/09 by Eduard Emelyanov, Emelyanov, Eduard
Mathematics · #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2312.05685

openalex publication_date 2023/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that an order continuous Banach lattice E is a KB-space if and only if each positive compact operator on E is a KB operator. We give conditions on quasi-KB (resp., quasi-Levi) operators to be KB (resp., Levi), study norm completeness and domination for these operators, and show that neither KB nor Levi operators are stable under rank one perturbations.

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