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BOUNDARY-CHAOTIC BEHAVIOUR OF CONTINUOUS FUNCTIONS UNDER THE ACTION OF OPERATORS

Published online by Cambridge University Press:  04 July 2003

Luis Bernal-González  and
María del Carmen Calderón-Moreno
Luis Bernal-González
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Avenida Reina Mercedes, 41080 Sevilla, Spain (lbernal@us.es; mccm@us.es)
María del Carmen Calderón-Moreno
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Avenida Reina Mercedes, 41080 Sevilla, Spain (lbernal@us.es; mccm@us.es)
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Abstract

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In this paper we introduce two classes of operators on spaces of continuous functions with values in $F$-spaces under the action of which many functions behave chaotically near the boundary. Several examples—including onto linear operators, left and right composition operators, multiplication operators, and operators with pointwise dense range or with some stability property—are given. This new theory extends one recently developed on spaces of holomorphic functions.

AMS 2000 Mathematics subject classification: Primary 47B38. Secondary 30D40; 46E10; 54D45

Keywords

omnipresent operatorDI-operatorspaces of continuous functionscluster setboundary-chaotic functioncomposition operator
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 2 , June 2003 , pp. 451 - 464
Copyright
Copyright © Edinburgh Mathematical Society 2003