The Blum–Hanson property for $\mathcal C(K)$ spaces

Pascal Lefèvre and Étienne Matheron

Vol. 282 (2016), No. 1, 203–212

DOI: 10.2140/pjm.2016.282.203

Abstract

We show that if $K$ is a compact metrizable space, then the Banach space $\mathcal{C}\left(K\right)$ has the so-called Blum–Hanson property exactly when $K$ has finitely many accumulation points. We also show that the space ${\ell }_{\infty }\left(\mathbb{N}\right)=\mathcal{C}\left(\beta \mathbb{N}\right)$ does not have the Blum–Hanson property.

Keywords

Blum–Hanson property, spaces of continuous functions, Stone–Čech compactification

Mathematical Subject Classification 2010

Primary: 46E15, 47A35

Secondary: 46B25

Milestones

Received: 7 December 2014

Accepted: 24 August 2015

Published: 24 February 2016