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arXiv · 2312.05685

On KB and Levi operators in Banach lattices

Eduard Emelyanov
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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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Eduard Emelyanov. 2023-12-09. On KB and Levi operators in Banach lattices. https://arxiv.org/abs/2312.05685

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