L-Dunford-Pettis property in Banach spaces
A. Retbi, B. El Wahbi
TL;DR
This paper introduces the L-Dunford-Pettis property in Banach spaces, characterizes it through geometric properties, and explores operator complementability related to this property.
Contribution
It presents a new property in Banach space theory, providing characterizations and operator analysis that extend existing geometric and functional analysis frameworks.
Findings
Characterization of L-Dunford-Pettis property via geometric properties
Identification of conditions for operator complementability
Extension of Dunford-Pettis concepts to new Banach space classes
Abstract
In this paper, we introduce and study the concept of L-Dunford-Pettis sets and L-Dunford-Pettis property in Banach spaces. Next, we give a characterization of the L-Dunford-Pettis property with respect to some well-known geometric properties of Banach spaces. Finally, some complementability of operators on Banach spaces with the L-Dunford-Pettis property are also investigated
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Taxonomy
TopicsAdvanced Banach Space Theory · Optimization and Variational Analysis · Fixed Point Theorems Analysis