Vol. 301, No. 2, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Vol. 296: 1  2
Vol. 295: 1  2
Vol. 294: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
New applications of extremely regular function spaces

Trond A. Abrahamsen, Olav Nygaard and Märt Põldvere

Vol. 301 (2019), No. 2, 385–394
DOI: 10.2140/pjm.2019.301.385
Abstract

Let L be an infinite locally compact Hausdorff topological space. We show that extremely regular subspaces of C0(L) have very strong diameter 2 properties and, for every real number ε with 0 < ε < 1, contain an ε-isometric copy of c0. If L does not contain isolated points they even have the Daugavet property, and thus contain an asymptotically isometric copy of 1.

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