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Extension operators on balls and on spaces of finite sets

Volume 227 / 2015

Antonio Avilés, Witold Marciszewski Studia Mathematica 227 (2015), 165-182 MSC: Primary 46B26, 46E15, 54C35, 54H05. DOI: 10.4064/sm227-2-6

Abstract

We study extension operators between spaces of continuous functions on the 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 $T: C(\lambda B_H)\to C(\mu B_H)$.

Authors

  • Antonio AvilésDepartamento de Matemáticas
    Universidad de Murcia
    30100 Murcia, Spain
    e-mail
  • Witold MarciszewskiInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    e-mail

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