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Abstract. For a separable rearrangement invariant space X on (0,∞) of fundamental type we identify the set of all p ∈ [1,∞] such that l is finitely represented in X… Click to show full abstract
Abstract. For a separable rearrangement invariant space X on (0,∞) of fundamental type we identify the set of all p ∈ [1,∞] such that l is finitely represented in X in such a way that the unit basis vectors of l (c0 if p = ∞) correspond to pairwise disjoint and equimeasurable functions. This characterization hinges upon a description of the set of approximate eigenvalues of the doubling operator x(t) 7→ x(t/2) in X . We prove that this set is surprisingly simple: depending on the values of some dilation indices of such a space, it is either an interval or a union of two intervals. We apply these results to the Lorentz and Orlicz spaces.
Journal Title: Mathematische Annalen
Year Published: 2021
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