Eduard Emelyanov
Published 2023-12-09Version 1
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.
A representation theorem for order continuous Banach lattices
The $oτ$-continuous, Lebesgue, KB, and Levi operators between vector lattices and topological vector spaces
Weakly compactly generated Banach lattices
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