Compactness of operators acting from a Lorentz sequence space to an Orlicz sequence space

Abstract

LetX and Y be closed subspaces of the Lorentz sequence space d(v, p) and the Orlicz sequence space l_M, respectively. It is proved that every bounded linear operator from X to Y is compact whenever $p > \beta _M : = \inf \{ q > 0:\inf \{ M(\lambda t)/M(\lambda )t^q :0< \lambda ,t \leqslant 1\} > 0.$ As an application, the reflexivity of the space of bounded linear operators acting from d(v, p) to l_M is characterized.