Linear functionals on orlicz spaces: General theory

Abstract

Let ∅ be a generalized Young’s function and L∅ the corresponding Orlicz space, on a general measure space. The problem considered here is the characterization of the dual space (L∅)*, in terms of integral representations, without any further restrictions. A complete solution of the problem is presented in this paper. If ∅ is continuous and the measure space is sigma finite (or localizable), then a characterization of the second dual (L∅)* * is also given. A detailed account of the quotient spaces of L* relative to certain subspaces is presented; and the analysis appears useful in the study of such spaces as the Riesz and K the-Toeplitz spaces. © 1968 by Pacific Journal of Mathematics.