The Volterra operator is not supercyclic
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2004
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Birkhauser Verlag
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Gallardo Gutiérrez, E. A. & Montes Rodríguez, A. «The Volterra Operator Is Not Supercyclic». Integral Equations and Operator Theory, vol. 50, n.o 2, octubre de 2004, pp. 211-16. DOI.org (Crossref), https://doi.org/10.1007/s00020-003-1227-y.
Abstract
It is shown that the classical Volterra operator, which is cyclic, is not supercyclic on any of the spaces L-p[0, 1], 1 less than or equal to p < infinity. This solves a question posed by Hector Salas. This contrasts with the fact that the derivative operator, the left inverse of the Volterra operator, although unbounded, is hypercyclic on L-p[0, 1].