Regular matrix methods of summability and real interpolation

Abstract

We show that the Banach-Saks property with respect to a regular positive matrix method of summability is inherited by the real interpolation spaces from a space forming the interpolation family and possessing this property. The proof refers to the Galvin-Prikry theorem on Ramsey sets. The results apply to several matrix methods of summability, such as Cesàro, Nørlund or Hölder methods.