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,...

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Detalles Bibliográficos
Autores: Bernal González, Luis, Calderón Moreno, María del Carmen
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
Descripción
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.