PreprintCC BY-NC-ND 4.0arXiv
DW-L-Weakly Compact Operators Between Banach Lattices
Abstract
In this paper we introduce a class of operators which we call DW-L-weakly compact operators. They carry disjointly weakly compact subsets of a Banach lattice onto L-weakly compact sets. The class of DW-L-weakly compact operators is closely related to two recently introduced classes of operators: almost L-weakly compact operators and order L-weakly compact operators. We show that DW-L-weakly compact operators are precisely those operators which are both almost L-weakly compact and order L-weakly compact. The adjoint and the order structure of DW-L-weakly compact operators are also considered.
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BibTeX
@misc{chen2026dwlweakly,
title = {{$DW$-$L$-Weakly Compact Operators Between Banach Lattices}},
author = {Jin Xi Chen and Qiaozhi Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34981},
eprint = {2610.34981},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34981},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - DW-L-Weakly Compact Operators Between Banach Lattices
AU - Jin Xi Chen
AU - Qiaozhi Wang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.34981
UR - https://arxiv.org/abs/2610.34981
AB - In this paper we introduce a class of operators which we call DW-L-weakly compact operators. They carry disjointly weakly compact subsets of a Banach lattice onto L-weakly compact sets. The class of DW-L-weakly compact operators is closely related to two recently introduced classes of operators: almost L-weakly compact operators and order L-weakly compact operators. We show that DW-L-weakly compact operators are precisely those operators which are both almost L-weakly compact and order L-weakly compact. The adjoint and the order structure of DW-L-weakly compact operators are also considered.
ER -