Extension operators on balls and on spaces of finite sets

Antonio Avilés; Witold Marciszewski

Extension operators on balls and on spaces of finite sets

Functional Analysis 2015-02-09 v1 General Topology

Authors: Antonio Avilés , Witold Marciszewski

Abstract

We study extension operators between spaces $\sigma_n(2^X)$ of subsets of $X$ of cardinality at most $n$ . As an application, we show that if $B_H$ is the unit ball of a nonseparable Hilbert space $H$ , equipped with the weak topology, then, for any $0<\lambda<\mu$ , there is no extension operator $T: C(\lambda B_H)\to C(\mu B_H)$ .

Keywords

extension operators spaces of finite sets unit ball nonseparable Hilbert space weak topology continuous functions cardinality

Cite

@article{arxiv.1502.01875,
  title  = {Extension operators on balls and on spaces of finite sets},
  author = {Antonio Avilés and Witold Marciszewski},
  journal= {arXiv preprint arXiv:1502.01875},
  year   = {2015}
}

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