Integral Equations and Operator Theory

, Volume 58, Issue 2, pp 153–173 | Cite as

Hypercyclic Pairs of Coanalytic Toeplitz Operators

Article

Abstract.

A pair of commuting operators, (A,B), on a Hilbert space \({\mathcal{H}}\) is said to be hypercyclic if there exists a vector \(x \in {\mathcal{H}}\) such that {AnBkx : n, k ≥ 0} is dense in \({\mathcal{H}}\) . If f, gH(G) where G is an open set with finitely many components in the complex plane, then we show that the pair (M*f, M*g) of adjoints of multiplcation operators on a Hilbert space of analytic functions on G is hypercyclic if and only if the semigroup they generate contains a hypercyclic operator. However, if G has infinitely many components, then we show that there exists f, gH(G) such that the pair (M*f, M*g) is hypercyclic but the semigroup they generate does not contain a hypercyclic operator. We also consider hypercyclic n-tuples.

Mathematics Subject Classification (2000).

Primary 47A16 Secondary 47B20 

Keywords.

Hypercyclic supercyclic semigroup 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Mathematics DepartmentWashington & Lee UniversityLexingtonUSA

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