Abstract
In this chapter, we study conditions of separability for Orlicz spaces L Φ . We consider Young classes Y Φ , the subspaces H Φ , and their embeddings H Φ ⊆ Y Φ ⊆ L Φ . We show that the equality H Φ = Y Φ = L Φ is equivalent to separability of L Φ . This and other equivalents of separability studied earlier in Chaps. 6 and 7 can be expressed in term of an Orlicz function Φ. The (Δ 2) condition is described to this end in detail.
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© 2016 Springer International Publishing Switzerland
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Rubshtein, BZ.A., Grabarnik, G.Y., Muratov, M.A., Pashkova, Y.S. (2016). Separable Orlicz Spaces. In: Foundations of Symmetric Spaces of Measurable Functions. Developments in Mathematics, vol 45. Springer, Cham. https://doi.org/10.1007/978-3-319-42758-4_14
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DOI: https://doi.org/10.1007/978-3-319-42758-4_14
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42756-0
Online ISBN: 978-3-319-42758-4
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