Local approach to order continuity in Cesaro function spaces

The goal of this paper is to present a complete characterization of points of order continuity in abstract Cesko function spaces CX for X being a symmetric function space. Under some additional assumptions mentioned result takes the form (CX)(a) = C(X-a). We also find simple equivalent condition for this equality which in the case of I = [0,1] comes to X not equal L-infinity Furthermore, we prove that X is order continuous if and only if CX is, under assumption that the Cesaro operator is bounded on X. This result is applied to particular spaces, namely: Cesko-Orlicz function spaces, Cesaro-Lorentz function spaces and Cesro-Marcinkiewicz function spaces to get criteria for OC-points. (C) 2017 Elsevier Inc. All rights reserved.