Non-supercyclicity of Volterra Convolution and Related Operators |
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Authors: | S P Eveson |
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Institution: | (1) Department of Mathematics, University of York, Heslington, York, YO10 5DD, England |
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Abstract: | We show that if V
α (α > 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
α 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-Gutiérrez and Montes-Rodríguez to show that V is not supercyclic. |
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Keywords: | " target="_blank"> Supercyclic Volterra convolution fractional integration operator |
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