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ArticleOriginal scientific text

Title

Universal images of universal elements

Authors 1

Affiliations

  1. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Sevilla 41080, Spain.

Abstract

We furnish several necessary and sufficient conditions for the following property: For a topological space X, a continuous selfmapping S of X and a family τ of continuous selfmappings of X, the image under S of every τ-universal element is also τ-universal. An application in operator theory, where we extend results of Bourdon, Herrero, Bes, Herzog and Lemmert, is given. In particular, it is proved that every hypercyclic operator on a real or complex Banach space has a dense invariant linear manifold with maximal algebraic dimension consisting, apart from zero, of vectors which are hypercyclic.

Keywords

ENG
universal element, almost commutativity, universal image, dense range, dense hypercyclic manifold, point spectrum of the adjoint, analytic function of an operator, real entire function, maximal dimension

Bibliography

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Studia Mathematica
2000/138/3
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Pages:
241-250
Main language of publication
English
Received
1998-09-18
Accepted
1999-01-22
Published
2000
Exact and natural sciences