Universality and chaos for tensor products of operators

We give sufficient conditions for the universality of tensor products {T n ⊗R n : n∈ N} of sequences of operators defined on Fréchet spaces. In particular we study when the tensor product T ⊗R of two operators is chaotic in the sense of Devaney. Applications are given for natural operators on functi...

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Bibliographic Details
Published in:Journal of approximation theory 2003-09, Vol.124 (1), p.7-24
Main Authors: Martı́nez-Giménez, Félix, Peris, Alfredo
Format: Article
Language:English
Subjects:
Chaotic dynamics
Hypercyclic vectors
Tensor products of operators
Universality
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Summary:We give sufficient conditions for the universality of tensor products {T n ⊗R n : n∈ N} of sequences of operators defined on Fréchet spaces. In particular we study when the tensor product T ⊗R of two operators is chaotic in the sense of Devaney. Applications are given for natural operators on function spaces of several variables, in Infinite Holomorphy, and for multiplication operators on the algebra L( E) following the study of Kit Chan.
ISSN:0021-9045
1096-0430
DOI:10.1016/S0021-9045(03)00118-7