# Universal images of universal elements

Studia Mathematica (2000)

- Volume: 138, Issue: 3, page 241-250
- ISSN: 0039-3223

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topBernal-González, Luis. "Universal images of universal elements." Studia Mathematica 138.3 (2000): 241-250. <http://eudml.org/doc/216702>.

@article{Bernal2000,

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.},

author = {Bernal-González, Luis},

journal = {Studia Mathematica},

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; univeral images; universal elements; hypercyclic operator; dense invariant subspace of maximal algebraic dimension; hypercyclic vectors; Weierstraß factorization theorem},

language = {eng},

number = {3},

pages = {241-250},

title = {Universal images of universal elements},

url = {http://eudml.org/doc/216702},

volume = {138},

year = {2000},

}

TY - JOUR

AU - Bernal-González, Luis

TI - Universal images of universal elements

JO - Studia Mathematica

PY - 2000

VL - 138

IS - 3

SP - 241

EP - 250

AB - 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.

LA - eng

KW - 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; univeral images; universal elements; hypercyclic operator; dense invariant subspace of maximal algebraic dimension; hypercyclic vectors; Weierstraß factorization theorem

UR - http://eudml.org/doc/216702

ER -

## References

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