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arXiv · 2005.11409

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

Driss Lhaimer·Khalid Bouras·Mohammed Moussa
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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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Driss Lhaimer, Khalid Bouras, Mohammed Moussa. 2020-05-22. On the class of order L-weakly and order M-weakly compact operators. https://arxiv.org/abs/2005.11409

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