Disjointly homogeneous Orlicz spaces revisited

2020/05/10 by Astashkin, Sergey
#46B42 #46B70 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2005.04640

Abstract

Let 1≤ p≤∞. 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 ℓ_p. We revisit DH-properties of Orlicz spaces and refine some previous results of this topic, showing that (p-DH)-property is not stable 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 DH-property.

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