Abstract
This paper is devoted to three properties of Banach lattices related to positively limited sets, which are called the positively limited Schur property of order p \((1 \le p \le \infty );\) that is, spaces on which every weakly p-compact and positively limited set is relatively compact, the positive DP\(^*\) property of order p and the weak positively limited Schur property of order p, respectively. The relationship between these three properties and other known properties, such as Schur property of order p, positive Schur property of order p, and positive Gelfand–Phillips property is studied. In particular, it is proved that the weak positively limited Schur property of order p coincides with the order continuity of the norm.
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Communicated by Marcel de Jeu.
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Ardakani, H., Amjadi, K. On the positively limited p-Schur property in Banach lattices. Ann. Funct. Anal. 14, 68 (2023). https://doi.org/10.1007/s43034-023-00292-y
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DOI: https://doi.org/10.1007/s43034-023-00292-y