Co-analytic, right-invertible operators are supercyclic

Volume 119 / 2010

Sameer Chavan Colloquium Mathematicum 119 (2010), 137-142 MSC: Primary 47A16; Secondary 47B20. DOI: 10.4064/cm119-1-9

Abstract

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.

Authors

  • Sameer ChavanDepartment of Mathematics and Statistics
    Indian Institute of Technology, Kanpur
    Kanpur 208016, India
    e-mail

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