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

• Author(s): Eva A. Gallardo-Gutieŕrez, Alfonso Montes-Rodríguez,
• Publisher: American Mathematical Soc.
• Pages: 81
• ISBN_10: 0821834320
  ISBN_13: 9780821834329
  
• Language: en
• Categories: Mathematics / Calculus , Mathematics / Mathematical Analysis , Mathematics / Functional Analysis , Mathematics / Complex Analysis ,

Description:... 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