Representation of linear functionals on a class of normed Köthe spaces

AbstractUnder the condition that Lθ,s∗, (the set of singular functionals on a normed Köthe space Lθ) is an abstract L-space, it is proved in this paper that there exists a set of purely finitely additive measures Mθ such that Lθ,s∗≅ holds. It follows that Lθ,s∗ is an abstract L-space if and only if Lθ,s∗ is Riesz isomorphic and isometric with a band in L∞,s∗