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Non-supercyclicity of Volterra convolution and related operators
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| Journal | Integral Equations and Operator Theory |
|---|---|
| Date | Published - Dec 2008 |
| Issue number | 4 |
| Volume | 62 |
| Number of pages | 5 |
| Pages (from-to) | 585-589 |
| Original language | English |
Abstract
We show that if V-alpha (alpha > 0) is the Riemann-Liouville fractional integration operator and T is an invertible operator on L-2(0, 1) which commutes with V, then TV alpha is not supercyclic on L-2(0, 1); in particular, many Volterra convolution operators are not supercyclic. The technique is based on an argument used by Gallardo-Gutierrez and Montes-Rodriguez to show that V is not supercyclic.
- Supercyclic, Volterra convolution, fractional integration operator
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