The Role of the Spectrum in the Cyclic Behavior of Composition Operators

Download or read book The Role of the Spectrum in the Cyclic Behavior of Composition Operators written by Eva A. Gallardo-Gutieŕrez and published by . This book was released on 2014-09-11 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: A bounded operator $T$ acting on a Hilbert space $\mathcal H$ is called cyclic if there is a vector $x$ such that the linear span of the orbit $\{T DEGREESn x: n \geq 0 \}$ is dense in $\mathcal H$. If the scalar multiples of the orbit are dense, then $T$ is called supercyclic. Finally, if the orbit itself is dense, then $T$ is called hyper