Holomorphic operators generating dense images

The existence of infinite dimensional closed linear spaces of holomorphic functions f on a domain G in the complex plane such that T f has dense images on certain subsets of G, where T is a continuous linear operator, is analyzed. Necessary and sufficient conditions for T to have the latter property...

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Detalhes bibliográficos
Autores: Bernal González, Luis, Calderón Moreno, María del Carmen, Prado Bassas, José Antonio
Formato: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2008
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/45726
Acesso em linha:http://hdl.handle.net/11441/45726
https://doi.org/10.1007/s00020-007-1547-4
Access Level:acceso abierto
Palavra-chave:Dense images
Infinite dimensional closed linear spaces
Non-relatively compact subsets
Residual sets
Differential operators
Composition operators
Multiplication operators
Descrição
Resumo:The existence of infinite dimensional closed linear spaces of holomorphic functions f on a domain G in the complex plane such that T f has dense images on certain subsets of G, where T is a continuous linear operator, is analyzed. Necessary and sufficient conditions for T to have the latter property are provided and applied to obtain a number of concrete examples: infinite order differential operators, composition operators and multiplication operators, among others.Key words and phrases: dense images, infinite dimensional closed linear spaces, non-relatively compact subsets, residual sets, differential operators, composition operators, multiplication operators.