Aron-Berner extensions of almost Dunford-Pettis multilinear operators
Geraldo Botelho, Luis Alberto Garcia
TL;DR
This paper investigates conditions under which Aron-Berner extensions of almost Dunford-Pettis multilinear operators preserve the almost Dunford-Pettis property across Banach lattices, supported by illustrative examples.
Contribution
It establishes new criteria for Aron-Berner extensions of multilinear operators to retain the almost Dunford-Pettis property in Banach lattices.
Findings
Conditions identified for preservation of almost Dunford-Pettis property
Extensions maintain property under specific lattice conditions
Examples illustrate the applicability of the results
Abstract
We prove several results establishing conditions on the Banach lattices E_1,..., E_m and F so that the Aron-Berner extensions of (separately) almost Dunford-Pettis m-linear operators from E_1 x ... x E_m to F are (separately) almost Dunford-Pettis. Illustrative examples are provided.
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Taxonomy
TopicsAdvanced Banach Space Theory · Optimization and Variational Analysis · Approximation Theory and Sequence Spaces