# Continuous operators for unbounded convergence in Banach lattices

## TL;DR

This paper explores the continuity of operators in Banach lattices concerning various types of unbounded convergence, providing new characterizations and insights into their approximation properties and compactness.

## Contribution

It introduces new characterizations of operator continuity for unbounded convergences and examines order-weakly compact operators in Banach lattices.

## Key findings

- Characterizations of operator continuity for uo, un, uaw, uaw* convergences
- Approximation properties of continuous operators for unbounded convergence
- Results on order-weakly compact operators in Banach lattices

## 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.