Perturbation Method in Orlicz Sequence Spaces

Abstract

We develop a new perturbation method in Orlicz sequence spaces ${\ell }_M$ with Orlicz function $M$ satisfying ${\Delta }_2$ condition at zero. This result allows one to support from below any bounded below lower semicontinuous function with bounded support, with a perturbation of the defining function ${\sigma }_M$. We give few examples how the method can be used for determining the type of the smoothness of certain Orlicz spaces.