Author:
Aurora Valles University of Cádiz Department of Mathematics Avda. de la Universidad s/n 11402 Jerez de la Frontera Spain

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Let T be an operator on a separable Hilbert space H , then it is called supercyclic if there exists an xH , (called supercyclic vector for T ) such that the set { λTnx : λ ∊ ℂ} is dense in H . Let T = ( T1 , ..., TN ) be a system of N commuting contractions defined on a separable Hilbert space, in this article we will show that if there exists at least a point of the Harte spectrum on
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{T}^N$$ \end{document}
(where
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{T}$$ \end{document}
is the unit circle), then there exists a vector such that is not supercyclic for any of the N -contractions. This result complements recent results of M. Kosiek and A. Octavio (see [4]) and extend results in [7].
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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation
1966
Volumes
per Year
1
Issues
per Year
4
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
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H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)