Embedding Orlicz Sequence Spaces into $C(α)$

Details Embedding Orlicz Sequence Spaces into $C(α)$ Embedding Orlicz Sequence Spaces into $C(α)$

1994-02-11

arxiv.org/abs/math/9402208v1

Mathematics

Functional Analysis

Scientific paper

Let $M$ be a non-degenerate Orlicz function such that there exist $\ep > 0$
and $0 < s < 1$ with $\su M(\ep s^i)/M(s^i) < \infty$. It is shown that the
Orlicz sequence space $h_M$ is isomorphic to a subspace of $C(\om^\om)$. It is
also shown that for any non-degenerate Orlicz function $M$, $h_M$ does not
embed into $C(\al)$ for any $\al < \om^\om$.

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