Article
Optimal extensions for positive order continuous operators on Banach functions spaces
Author/s | Delgado Garrido, Olvido |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2014 |
Deposit Date | 2021-01-11 |
Published in |
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Abstract | In 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 ... In 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. |
Funding agencies | Ministerio de Economía y Competitividad (MINECO). España Junta de Andalucía |
Project ID. | MTM2012-36732- C03-03
FQM-262 FQM-4643 FQM-7276 |
Citation | Delgado Garrido, O. (2014). Optimal extensions for positive order continuous operators on Banach functions spaces. Glasgow Mathematical Journal, 56 (3), 481-501. |
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