Polynomial automorphisms and hypercyclic operators on spaces of analytic functions |
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Authors: | Zoryana Novosad Andriy Zagorodnyuk |
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Affiliation: | (1) Institute for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, 3 b, Naukova str., Lviv, 79060, Ukraine |
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Abstract: | We consider hypercyclic composition operators on which can be obtained from the translation operator using polynomial automorphisms of . In particular we show that if C S is a hypercyclic operator for an affine automorphism S on , then for some polynomial automorphism Θ and vectors a and b, where I is the identity operator. Finally, we prove the hypercyclicity of “symmetric translations” on a space of symmetric analytic functions on ℓ1. Received: 8 June 2006 Revised: 26 September 2006 |
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Keywords: | Primary: 47A16 Secondary: 46E10, 46E50 |
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