Integral Equations and Operator Theory

, Volume 58, Issue 2, pp 153–173

Hypercyclic Pairs of Coanalytic Toeplitz Operators


DOI: 10.1007/s00020-007-1484-2

Cite this article as:
Feldman, N.S. Integr. equ. oper. theory (2007) 58: 153. doi:10.1007/s00020-007-1484-2


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 47A16Secondary 47B20



Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Mathematics DepartmentWashington & Lee UniversityLexingtonUSA