2021-01-112021-01-112014Delgado Garrido, O. (2014). Optimal extensions for positive order continuous operators on Banach functions spaces. Glasgow Mathematical Journal, 56 (3), 481-501.0017-0895https://hdl.handle.net/11441/103503In this paper we give conditions under which a positive order continuous operator T defined on a Banach function space can be extended, preserving the order continuity in a certain optimal way. The optimal domain for T turns out to be a space of weakly integrable functions with respect to a vector measure (defined on a δ-ring) canonically associated to T. A similar result is obtained when T is σ-order continuous and we want to preserve the σ-order continuity. We apply these results to kernel operators.application/pdf21engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1017/S0017089513000384