2021-01-082021-01-082015Delgado Garrido, O. y Sánchez Pérez, E.A. (2015). Optimal domain of q-concave operators and vector measure representation of q-concave Banach lattices. ArXiv.org, arXiv:1511.02337https://hdl.handle.net/11441/103469Given a Banach space valued q-concave linear operator T defined on a σ-order continuous quasi-Banach function space, we provide a description of the optimal domain of T preserving q-concavity, that is, the largest σ-order continuous quasi-Banach function space to which T can be extended as a q-concave operator. We show in this way the existence of maximal extensions for q-concave operators. As an application, we show a representation theorem for q-concave Banach lattices through spaces of integrable functions with respect to a vector measure. This result culminates a series of representation theorems for Banach lattices using vector measures that have been obtained in the last twenty years.application/pdf21engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Banach latticesq-concave operatorsQuasi-Banach function spacesVector measures defined on a δ-ringinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess