Journal of Operator Theory
Volume 62, Issue 1, Summer 2009 pp. 199-214.
Cyclic vectors and invariant subspaces for Bergman and Dirichlet shiftsAuthors: Eva A. Gallardo-Gutierrez (1), Jonathan R. Partington (2), and Dolores Segura (3)
Author institution: (1) Departamento de Matematicas, Universidad de Zaragoza e IUMA, Plaza San Francisco s/n, 50009 Zaragoza, Spain
(2) School of Mathematics, Univ. of Leeds, Leeds LS2 9JT, U.K.
Summary: It is shown that the invariant subspaces for the Bergman and Dirichlet shifts on the right half-plane correspond to the common invariant subspaces of the right shift operators on certain weighted Lebesgue spaces on the half-line. As a particular instance, the corresponding result for invariant subspaces of multipliers induced by weak-star generators of $\mathcal {H}^{\infty}(\mathbb{D})$ on weighted Bergman spaces of the unit disc is deduced. Finally, cyclic vectors for the Bergman and Dirichlet shifts are also studied.
Contents Full-Text PDF