Compact subsets of $\Ps(\N)$ with applications to the embedding of symmetric sequence spaces into $C(\alpha)$

Denny H. Leung

Compact subsets of $\Ps(\N)$ with applications to the embedding of symmetric sequence spaces into $C(\alpha)$

Functional Analysis 2009-09-25 v1

Authors: Denny H. Leung

Abstract

Let $\Ps(\N)$ be the set of all finite subsets of $\N$ , endowed with the product topology. A description of the compact subsets of $\Ps(\N)$ is given. Two applications of this result to Banach space theory are shown : (1) a characterization of the symmetric sequence spaces which embed into $C(\om^\om)$ , and (2) a characterization, in terms of the Orlicz function $M$ , of the Orlicz sequence spaces $h_M$ which embed into $C(K)$ for some countable compact Hausdorff space $K$ .

Keywords

compact subset symmetric sequence space banach space embedding orlicz sequence space product topology

Cite

@article{arxiv.math/9610212,
  title  = {Compact subsets of $\Ps(\N)$ with applications to the embedding of symmetric sequence spaces into $C(\alpha)$},
  author = {Denny H. Leung},
  journal= {arXiv preprint arXiv:math/9610212},
  year   = {2009}
}

Related papers

View all related →