Orlicz sequence spaces without local convexity

Abstract

In this paper we continue the study of Orlicz sequence spaces initiated by Lindberg (5) and Lindenstrauss and Tzafriri (7), (8) and (9). Our main concern is to investigate features of the theory which occur when the restriction of local convexity is lifted. It is clear that some results will hold with identical proofs, at least when the space is locally bounded. However, we are chiefly interested in the differences which arise. We always assume that the Orlicz function F satisfies the Δ2-condition.