#### 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 $\mathsc{C}\left(K\right)$ has the so-called Blum–Hanson property exactly when $K$ has finitely many accumulation points. We also show that the space ${\ell }_{\infty }\left(ℕ\right)=\mathsc{C}\left(\beta ℕ\right)$ 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