Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

Streszczenie

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.