Continuous Operators for Unbounded Convergence in Banach Lattices

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 uo, un, uaw and uaw*-convergence. Based on these results, we discuss the order-weakly compact operators on Banach lattices.

Automated summary

In this paper, the authors study the issue of unbounded convergence in Banach lattices and discuss the approximation property and continuity characterization of continuous operators. They also analyze the properties of order-weakly compact operators on Banach lattices.