A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Compactifications of $\omega $ and the Banach space $c_0$

Volume 237 / 2017

Piotr Drygier, Grzegorz Plebanek Fundamenta Mathematicae 237 (2017), 165-186 MSC: Primary 46B26, 46E50, 54D35; secondary 28C15, 03E50. DOI: 10.4064/fm263-6-2016 Published online: 9 December 2016

Abstract

We investigate for which compactifications $\gamma \omega $ of the discrete space of natural numbers $\omega $, the natural copy of the Banach space $c_0$ is complemented in $C(\gamma \omega )$. We show, in particular, that the separability of the remainder $\gamma \omega \setminus \omega $ is neither sufficient nor necessary for $c_0$ to be complemented in $C(\gamma \omega )$ (the latter result is proved under the continuum hypothesis). We analyse, in this context, compactifications of $\omega $ related to embeddings of the measure algebra into $P(\omega )/\mathop {\rm fin}\nolimits $.

We also prove that a Banach space $C(K)$ contains a rich family of complemented copies of $c_0$ whenever the compact space $K$ admits only measures of countable Maharam type.

Authors

  • Piotr DrygierInstytut Matematyczny
    Uniwersytet Wrocławski
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail
  • Grzegorz PlebanekInstytut Matematyczny
    Uniwersytet Wrocławski
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image