Universal images of universal elements

• Autorzy: Luis Bernal-González
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 54C10: Special maps on topological spaces (open, closed, perfect, etc.)
• 47A16: Cyclic vectors, hypercyclic and chaotic operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2000
• Tom: 138
• Numer: 3
• Strony: 241-250

Daty

wydano

2000

otrzymano

1998-09-18

poprawiono

1999-01-22

Twórcy

autor

Luis Bernal-González

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

Bibliografia

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