THE BLUM-HANSON PROPERTY FOR C(K) SPACES

Pascal Lefèvre (1) , Etienne Matheron (1)

1 LML - Laboratoire de Mathématiques de Lens

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 $\ell^\infty$ does not have the Blum-Hanson property.

Mots clés: Blum-Hanson property; C(K) space; strongly mixing

Domaines: Analyse fonctionnelle [math.FA]

Pascal Lefèvre, Etienne Matheron. THE BLUM-HANSON PROPERTY FOR C(K) SPACES. 2014. ⟨hal-00990096⟩