Strongly omnipresent operators: general conditions and applications to composition operators
This paper studies the concept of strongly omnipresent operators that was recently introduced by the first two authors. An operator T on the space H(G) of holomorphic functions on a complex domain G is called strongly omnipresent whenever the set of T-monsters is residual in H(G), and a T-monster is...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2002 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/87495 |
| Acceso en línea: | https://hdl.handle.net/11441/87495 https://doi.org/10.1017/S1446788700036764 |
| Access Level: | acceso abierto |
| Palabra clave: | Holomorphic function T-monster Residual set Strongly omnipresent operator Dense range Locally dense range Locally stable operator Composition operator Leftcomposition operator Multiplication operator |
| Sumario: | This paper studies the concept of strongly omnipresent operators that was recently introduced by the first two authors. An operator T on the space H(G) of holomorphic functions on a complex domain G is called strongly omnipresent whenever the set of T-monsters is residual in H(G), and a T-monster is a function f such that T f exhibits an extremely ‘wild’ behaviour near the boundary. We obtain sufficient conditions under which an operator is strongly omnipresent, in particular, we show that every onto linear operator is strongly omnipresent. Using these criteria we completely characterize strongly omnipresent composition and multiplication operators. |
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