New applications of extremely regular function spaces

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 $ε$ with $0 < ε < 1$ , contain an $ε$ -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 $ℓ_{1}$ .

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Keywords

extremely regular function space, strong diameter 2 property, almost square space, octahedrality, Daugavet property

Mathematical Subject Classification 2010

Primary: 46B20, 46B22, 46B04

Milestones

Received: 2 November 2017

Revised: 25 September 2018

Accepted: 9 December 2018

Published: 24 October 2019

Authors

Trond A. Abrahamsen
Department of Mathematics University of Agder Kristiansand Norway

Olav Nygaard
Department of Mathematics University of Agder Kristiansand Norway

Märt Põldvere
Institute of Mathematics and Statistics University of Tartu Tartu Estonia

Vol. 301, No. 2, 2019

Trond A. Abrahamsen, Olav Nygaard and Märt Põldvere

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors