Some results on unbounded absolute weak Dunford-Pettis operators
Hui Li, Zili Chen
TL;DR
This paper characterizes Banach lattices where every Dunford-Pettis or weak Dunford-Pettis operator is also unbounded absolute weak Dunford-Pettis, establishing a connection between these classes of operators.
Contribution
It provides a characterization of Banach lattices based on the equivalence of Dunford-Pettis and unbounded absolute weak Dunford-Pettis operators.
Findings
Identifies conditions under which all Dunford-Pettis operators are unbounded absolute weak Dunford-Pettis
Establishes the converse relationship in specific Banach lattices
Contributes to the understanding of operator classes in Banach lattice theory
Abstract
In this paper, we characterize Banach lattices on which each Dunford-Pettis operator (or weak Dunford-Pettis) is unbounded absolute weak Dunford-Pettis operator and the converse.
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Taxonomy
TopicsAdvanced Banach Space Theory · Holomorphic and Operator Theory · Advanced Harmonic Analysis Research