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Disjointly homogeneous Orlicz spaces revisited

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Abstract

Let \(1 \le p \le \infty \). A Banach lattice X is said to be p-disjointly homogeneous or \((p-DH)\) (resp. restricted \((p-DH)\)) if every normalized disjoint sequence in X (resp. every normalized sequence of characteristic functions of disjoint subsets) contains a subsequence equivalent in X to the unit vector basis of \(\ell _p\). We revisit DH-properties of Orlicz spaces and refine some previous results of this topic, showing that the \((p-DH)\)-property is not stable under duality in the class of Orlicz spaces and the classes of restricted \((p-DH)\) and \((p-DH)\) Orlicz spaces are different. Moreover, we give a characterization of uniform \((p-DH)\) Orlicz spaces and establish also closed connections between this property and the duality of the DH-property.

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  1. Department of Mathematics, Samara National Research University, Moskovskoye shosse 34, 443086, Samara, Russia

    Sergey V. Astashkin

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  1. Sergey V. Astashkin
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Correspondence to Sergey V. Astashkin.

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The work was completed as a part of the implementation of the development program of the Scientific and Educational Mathematical Center Volga Federal District, agreement no. 075-02-2020-1488/1.

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Astashkin, S.V. Disjointly homogeneous Orlicz spaces revisited. Annali di Matematica 200, 2689–2713 (2021). https://doi.org/10.1007/s10231-021-01097-3

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  • DOI: https://doi.org/10.1007/s10231-021-01097-3

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