# Dynamics of perturbations of the identity operator by multiples of the backward shift on $l^{\infty}(\mathbb{N})$

Costakis G, Manoussos A, Nasseri AB (2013) .

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Abstract
Let $B$, $I$ be the unweighted backward shift and the identity operatorrespectively on $l^{\infty}(\mathbb{N})$, the space of bounded sequences overthe complex numbers endowed with the supremum norm. We prove that $I+\lambda B$is locally topologically transitive if and only if $|\lambda |>2$. This, showsthat a classical result of Salas, which says that backward shift perturbationsof the identity operator are always hypercyclic, or equivalently topologicallytransitive, on $l^p(\mathbb{N})$, $1\leq p<+\infty$, fails to hold for thenotion of local topological transitivity on $l^{\infty}(\mathbb{N})$. We alsoobtain further results which complement certain results from \cite{CosMa}.
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Costakis G, Manoussos A, Nasseri AB. Dynamics of perturbations of the identity operator by multiples of the backward shift on $l^{\infty}(\mathbb{N})$. 2013.
Costakis, G., Manoussos, A., & Nasseri, A. B. (2013). Dynamics of perturbations of the identity operator by multiples of the backward shift on $l^{\infty}(\mathbb{N})$
Costakis, G., Manoussos, A., and Nasseri, A. B. (2013). Dynamics of perturbations of the identity operator by multiples of the backward shift on $l^{\infty}(\mathbb{N})$.
Costakis, G., Manoussos, A., & Nasseri, A.B., 2013. Dynamics of perturbations of the identity operator by multiples of the backward shift on $l^{\infty}(\mathbb{N})$.
G. Costakis, A. Manoussos, and A.B. Nasseri, “Dynamics of perturbations of the identity operator by multiples of the backward shift on $l^{\infty}(\mathbb{N})$”, 2013.
Costakis, G., Manoussos, A., Nasseri, A.B.: Dynamics of perturbations of the identity operator by multiples of the backward shift on $l^{\infty}(\mathbb{N})$. (2013).
Costakis, George, Manoussos, Antonios, and Nasseri, Amir Bahman. “Dynamics of perturbations of the identity operator by multiples of the backward shift on $l^{\infty}(\mathbb{N})$”. (2013).
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arXiv 1302.1736