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On a class of universal Orlicz function spaces. (English) Zbl 0799.46030
J. Lindenstrauss and L. Tzafriri [Isr. J. Math. 11, 355–379 (1972; Zbl 0237.46034)] have given examples of universal Orlicz sequence space $$l^\Psi$$ for every Orlicz sequence spaces $$l^\varphi$$ with $$\varphi$$ an Orlicz function $$c$$-convex and $$d$$-concave for every $$1 \leq c < d < \infty$$ and it was proved that every space $$l^\varphi$$ is isomorphic to a complemented subspace of $$l^\Psi$$.
In this paper the author gives a class of universal Orlicz function spaces $$L^\Psi [0,1]$$, which are universal for a prefixed class of Orlicz sequence spaces $$l^\varphi$$ and the spaces $$l^\varphi$$ are also isomorphic to complemented subspaces of $$L^\Psi [0,1]$$.
As a consequence the author shows that every separable Nakano sequence space $$l^{(p_ n)}$$ can be isomorphically represented as a weighted Orlicz sequence space $$l^\Psi (w)$$ for a suitable Orlicz function $$\Psi$$ and some summable weight sequence $$w$$.
##### MSC:
 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46A45 Sequence spaces (including Köthe sequence spaces) 46B45 Banach sequence spaces
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