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arXiv · 1711.01494

New applications of extremely regular function spaces

Trond A. Abrahamsen·Olav Nygaard·Märt Põldvere
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Abstract

Let $L$ be an infinite locally compact Hausdorff topological space. We show that extremely regular subspaces of $C_0(L)$ have very strong diameter $2$ properties and, for every real number $\varepsilon$ with $0<\varepsilon<1$, contain an $\varepsilon$-isometric copy of $c_0$. If $L$ does not contain isolated points they even have the Daugavet property, and thus contain an asymptotically isometric copy of $\ell_1$.

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BibTeXRIS

Trond A. Abrahamsen, Olav Nygaard, Märt Põldvere. 2017-11-04. New applications of extremely regular function spaces. https://doi.org/10.2140/pjm.2019.301.385

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