Non-supercyclicity of Volterra convolution and related operators

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JournalIntegral Equations and Operator Theory
DatePublished - Dec 2008
Issue number4
Volume62
Number of pages5
Pages (from-to)585-589
Original languageEnglish

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.

    Research areas

  • Supercyclic, Volterra convolution, fractional integration operator

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