Strictly singular and nearly weakly compact operators in Banach function spaces

Abstract

0. INTRODUCTION In this note we discuss strictly singular and nearly weakly compact operators. The latter concept is a slight generalization of the notion of an almost weakly compact operator as defined by R. H. HERMAN [4]. We deduce a condition to the extent that a continuous linear integral operator from one Banach function space into another is strictly singular. In doing so we consider the concepts of almost reflexiveness and nearly weak compactness. Finally we’investigate the connection between these concepts and the concept of a o(L,, L,‘) compact operator. (For definitions see the subsequent sections).