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...
| Autores: | , , |
|---|---|
| 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 |
| 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. |
|---|