Reducing Subspaces on the Annulus

Details Reducing Subspaces on the Annulus Reducing Subspaces on the Annulus

2009-02-11

arxiv.org/abs/0902.1794v1

Mathematics

Functional Analysis

13 pages

Scientific paper

We study reducing subspaces for an analytic multiplication operator M_{z^{n}} on the Bergman space L_{a}^{2}(A_{r}) of the annulus A_{r}, and we prove that M_{z^{n}} has exactly 2^n reducing subspaces. Furthermore, in contrast to what happens for the disk, the same is true for the Hardy space on the annulus. Finally, we extend the results to certain bilateral weighted shifts, and interpret the results in the context of complex geometry.

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