Compactness of operators acting from a Lorentz sequence space to an Orlicz sequence space (Q1426888)

Let \(d\left( v,p\right) \) be the Lorentz sequence space and, for an Orlicz function \(M\), let \(l_{M}\) be the Orlicz sequence space. Define \(\beta _{M}=\inf \{ q>0: \inf \{ M( \lambda t)/ M (\lambda ) t^{q}: 0<\lambda ,t\leq 1\} >0\} \). The main result of the present paper is Theorem 2. Let \(X\) and \(Y\) be closed subspaces of \(d(v,p) \) and \( l_{M}\), respectively. If \(p>\beta _{M}\), then \(K(X,Y) = L(X,Y) \). The fact that the condition \(p>\beta _{M}\) is essential and some applications to the reflexivity of spaces of operators acting from \(d(v,p) \) to \(l_{M}\) are also given.