Continuous operators for unbounded convergence in Banach lattices
Functional Analysis
2021-04-06 v6
Abstract
Recently, the functionals different types of unbounded convergences (uo, un, uaw, uaw*) in Banach lattices were studied. In this paper, we study the continuous operators with respect to unbounded convergences. We first investigate the approximation property of continuous operators for unbounded convergence. Then we show some characterizations of the continuity of the continuous operators for uo, un, uaw and uaw*-convergence. Based on these results, we discuss the order-weakly compact operators on Banach lattices. Some related results are obtained as well.
Cite
@article{arxiv.1903.04854,
title = {Continuous operators for unbounded convergence in Banach lattices},
author = {Zhangjun Wang and Zili Chen and Jinxi Chen},
journal= {arXiv preprint arXiv:1903.04854},
year = {2021}
}