Co-analytic, right-invertible operators are supercyclic

Sameer Chavan¹

¹ Department of Mathematics and Statistics Indian Institute of Technology, Kanpur Kanpur 208016, India

Colloquium Mathematicum, Tome 119 (2010) no. 1, pp. 137-142.

Résumé

Let $\mathcal H$ denote a complex, infinite-dimensional, separable Hilbert space, and for any such Hilbert space $\mathcal H$, let ${\mathcal B}({\mathcal H})$ denote the algebra of bounded linear operators on $\mathcal H.$ We show that for any co-analytic, right-invertible $T$ in ${\mathcal B}({\mathcal H}),$ $\alpha T$ is hypercyclic for every complex $\alpha$ with $|\alpha|>\beta^{-1},$ where $\beta \equiv \inf_{\|x\|=1}\|T^*x\| > 0.$ In particular, every co-analytic, right-invertible $T$ in ${\mathcal B}({\mathcal H})$ is supercyclic.

Détail

DOI : 10.4064/cm119-1-9

Keywords: mathcal denote complex infinite dimensional separable hilbert space hilbert space mathcal mathcal mathcal denote algebra bounded linear operators mathcal co analytic right invertible mathcal mathcal alpha hypercyclic every complex alpha alpha beta where beta equiv inf *x particular every co analytic right invertible mathcal mathcal supercyclic