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Reducing Subspaces on the Annulus

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Abstract

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 2n 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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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA

    Ronald G. Douglas

  2. Department of Mathematics, University of Toledo, Toledo, OH, 43606-3390, USA

    Yun-Su Kim

Authors
  1. Ronald G. Douglas
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  2. Yun-Su Kim
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Correspondence to Yun-Su Kim.

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Research was partially supported by a grant from the National Science Foundation.

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Douglas, R.G., Kim, YS. Reducing Subspaces on the Annulus. Integr. Equ. Oper. Theory 70, 1–15 (2011). https://doi.org/10.1007/s00020-011-1874-3

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  • DOI: https://doi.org/10.1007/s00020-011-1874-3

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