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Published in:
2016 | OriginalPaper | Chapter
14. Separable Orlicz Spaces
Authors : Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
Published in: Foundations of Symmetric Spaces of Measurable Functions
Publisher: Springer International Publishing
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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.