Let
T
be an operator on a separable Hilbert space
H
, then it is called supercyclic if there exists an
x
∊
H
, (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}
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$$\mathbb{T}^N$$
\end{document} (where \documentclass{aastex}
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$$\mathbb{T}$$
\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].
Denseness of sets of supercyclic vectors
