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On the class of order L-weakly and order M-weakly compact operators

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Abstract

In this paper, we introduce and study new concepts of order L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms. It is proved that if \(T:E \longrightarrow F\) is an operator between two Banach lattices, then T is order M-weakly compact if and only if its adjoint \(T'\) is order L-weakly compact. Also, we show that if its adjoint \(T'\) is order M-weakly compact, then T is order L-weakly compact. Some related results are also obtained.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Ibn Tofail University, P.O. Box 133, 14000, Kenitra, Morocco

    Driss Lhaimer & Mohammed Moussa

  2. Department of Mathematics, Faculty Polydisciplinary, Abdelmalek Essaadi University, P.O. Box 745, 92004, Larache, Morocco

    Khalid Bouras

Authors
  1. Driss Lhaimer
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  2. Khalid Bouras
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  3. Mohammed Moussa
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Correspondence to Driss Lhaimer.

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Lhaimer, D., Bouras, K. & Moussa, M. On the class of order L-weakly and order M-weakly compact operators. Positivity 25, 1569–1578 (2021). https://doi.org/10.1007/s11117-021-00829-2

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  • DOI: https://doi.org/10.1007/s11117-021-00829-2

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