Continuous Operators for Unbounded Convergence in Banach Lattices

Zhangjun Wang and Zili Chen
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Zhangjun Wang: School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China
Zili Chen: School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China

Mathematics, 2022, vol. 10, issue 6, 1-7

Abstract: Recently, continuous functionals for unbounded order (norm, weak and weak*) 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 u o , u n , u a w and u a w * -convergence. Based on these results, we discuss the order-weakly compact operators on Banach lattices.

Keywords: Banach lattice; unbounded order convergence; unbounded norm convergence; unbounded absolute weak convergence; unbounded absolute weak* convergence; order-weakly compact operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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