Some translation-invariant Banach function spaces which contain $c_0$

Pascal Lefèvre (1) , Daniel Li (1) , Hervé Queffélec (2) , Luis Rodriguez-Piazza (3)

1 LML - Laboratoire de Mathématiques de Lens
2 LPP - Laboratoire Paul Painlevé
3 Departamento de Analisis Matematico

We produce several situations where some natural subspaces of classical Banach spaces of functions over a compact abelian group contain the space $c_0$.

Keywords: cotype; Hilbert set; invariant mean; Orlicz space; $q$-Rider set; Riemann-integrable function; Rosenthal set; set of uniform convergence; Sidon set; $p$-Sidon set

Domains: Functional Analysis [math.FA]

Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza. Some translation-invariant Banach function spaces which contain $c_0$. Studia Mathematica, 2004, 163 (2), pp.137 - 155. ⟨hal-00441506⟩