Title
Hypercyclicity of Shifts as a Zero-one Law of Orbital Limit Points
Publication Date
2012
Document Type
Article
Abstract
Summary: On a separable, infinite dimensional Banach space $X$, a bounded linear operator $T:X \rightarrow X$ is said to be \textit{hypercyclic} if there exists a vector $x$ in $X$ such that its orbit $\mathrm{Orb}(T,x)=\{x, Tx, T^2x, \ldots\}$ is dense in $X$. However, for a unilateral weighted backward shift or a bilateral weighted shift $T$ to be hypercyclic, we show that it suffices to merely require the operator to have an orbit $\mathrm{Orb}(T,x)$ with a non-zero limit point.
Original Citation
Chan, K., Seceleanu, I. (2012). Hypercyclicity of Shifts as a Zero-one Law of Orbital Limit Points. Journal of Operator Theory, 67(1), 257-277.
Virtual Commons Citation
Chan, Kit and Seceleanu, Irina (2012). Hypercyclicity of Shifts as a Zero-one Law of Orbital Limit Points. In Mathematics Faculty Publications. Paper 61.
Available at: https://vc.bridgew.edu/math_fac/61