Artículo
Dense linear manifolds of monsters
Autor/es | Bernal González, Luis
Calderón Moreno, María del Carmen |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2002-12 |
Fecha de depósito | 2019-06-19 |
Publicado en |
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Resumen | In this paper the new concept of totally omnipresent operators is introduced. These
operators act on the space of holomorphic functions of a domain in the complex plane.
The concept is more restrictive than that of ... In this paper the new concept of totally omnipresent operators is introduced. These operators act on the space of holomorphic functions of a domain in the complex plane. The concept is more restrictive than that of strongly omnipresent operators, also introduced by the authors in an earlier work, and both of them are related to the existence of functions whose images under such operators exhibit an extremely wild behaviour near the boundary. Sufficient conditions for an operator to be totally omnipresent as well as several outstanding examples are provided. After extending a statement of the first author about the existence of large linear manifolds of hypercyclic vectors for a sequence of suitable continuous linear mappings, it is shown that there is a dense linear manifold of holomorphic monsters in the sense of Luh, so completing earlier nice results due to Luh and Grosse-Erdmann. |
Identificador del proyecto | PB96-1348 |
Cita | Bernal González, L. y Calderón Moreno, M.d.C. (2002). Dense linear manifolds of monsters. Journal of Approximation Theory, 119 (2), 156-180. |
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