Continuous Operators for Unbounded Convergence in Banach Lattices

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 uo, un, uaw and uaw*-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