The Banach-Saks Properties in Orlicz-Lorentz Spaces

Abstract

The Banach-Saks index of an Orlicz-Lorentz space ${\mathrm{\Lambda }}_{\phi ,w}(I)$ for both function and sequence case, is computed with respect to its Matuszewska-Orlicz indices of $\phi$. It is also shown that an Orlicz-Lorentz function space has weak Banach-Saks (resp., Banach-Saks) property if and only if it is separable (resp., reflexive).