Vol. 282, No. 1, 2016

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

Pascal Lefèvre and Étienne Matheron

Vol. 282 (2016), No. 1, 203–212
Abstract

We show that if K is a compact metrizable space, then the Banach space C(K) has the so-called Blum–Hanson property exactly when K has finitely many accumulation points. We also show that the space () = C(β) 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
Authors
Pascal Lefèvre
Laboratoire de Mathématiques de Lens
Université d’Artois
Rue Jean Souvraz S.P. 18
62307 Lens
France
Étienne Matheron
Laboratoire de Mathématiques de Lens
Université d’Artois
Rue Jean Souvraz S.P. 18
62307 Lens
France