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Role of the Spectrum in the Cyclic Behavior of Composition Operators
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 $\{T^n x: n \geq 0 \}$ 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 cyclic.
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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 $\{T^n x: n \geq 0 \}$ 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 cyclic.
| ISBN / EAN | 9780821834329 |
|---|---|
| Editeur | American Mathematical Society |