Geodesic
Universal images of universal elements
Studia Mathematica, Tome 138 (2000) no. 3, pp. 241-250

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-138-3-241-250
Keywords: 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

Luis Bernal-González 1

1 
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Luis Bernal-González. Universal images of universal elements. Studia Mathematica, Tome 138 (2000) no. 3, pp. 241-250. doi: 10.4064/sm-138-3-241-250

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