Operators with dense images everywhere
In this paper, the authors introduce the dense-image operators T as those with a wild behaviour near of the boundary of a domain G, via certain subsets. The relationship with other kinds of operators with wild behaviour is studied, proving that the new concept generalizes the earlier of omnipresent,...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2001 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/87507 |
| Acceso en línea: | https://hdl.handle.net/11441/87507 https://doi.org/10.1006/jmaa.2001.7600 |
| Access Level: | acceso abierto |
| Palabra clave: | Dense-image operator Omnipresent operator Strongly omnipresent operator Differential operator Antidifferential operator Integral operator Holomorphic function Composition operator Left-composition operator Multiplication operator Local dense range Residual set Non-relatively compact set |
| Sumario: | In this paper, the authors introduce the dense-image operators T as those with a wild behaviour near of the boundary of a domain G, via certain subsets. The relationship with other kinds of operators with wild behaviour is studied, proving that the new concept generalizes the earlier of omnipresent, but there is no good relationship with the strongly omnipresent operators. We obtain, among other results, that the following kinds of operators are dense-image: onto linear operators; operators with local dense range satisfying soft conditions; Volterra complex integral operators plus infinite order differential operators, multiplication operators. In addition, holomorphic selfmappings and entire functions generating dense-image right or left composition operators are completely characterized. |
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