Applications for Unbounded Convergences in Banach Lattices

Author:

Wang ZhangjunORCID,Chen Zili

Abstract

Several recent papers investigated unbounded convergences in Banach lattices. The focus of this paper is to apply the results of unbounded convergence to the classical Banach lattice theory from a new perspective. Combining all unbounded convergences, including unbounded order (norm, absolute weak, absolute weak*) convergence, we characterize L-weakly compact sets, L-weakly compact operators and M-weakly compact operators on Banach lattices. For applications, we introduce so-called statistical-unbounded convergence and use these convergences to describe KB-spaces and reflexive Banach lattices.

Funder

National Natural Science Foundation of China

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Some properties of weak* Dunford-Pettis operators on Banach lattices;Boletim da Sociedade Paranaense de Matemática;2024-05-06

2. STATISTICAL UNBOUNDED ORDER CONVERGENCE IN RIESZ SPACES;Facta Universitatis, Series: Mathematics and Informatics;2022-09-20

3. un L- and M-weakly compact operators on Banach lattices;Positivity;2022-04-25

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