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Continuous Operators for Unbounded Convergence in Banach Lattices

Author

Listed:
  • Zhangjun Wang

    (School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China)

  • Zili Chen

    (School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China)

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.

Suggested Citation

  • Zhangjun Wang & Zili Chen, 2022. "Continuous Operators for Unbounded Convergence in Banach Lattices," Mathematics, MDPI, vol. 10(6), pages 1-7, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:966-:d:773599
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