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The majorization function and the index of invariant sub spaces in the Bergman spaces

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Abstract

The index of an invariant subspace ℳ of a Banach space of analytic functions in the open unit disc is defined by indℳ = dimℳ/zℳ. In this paper, we provide a strong link between high index and nontangential boundary behaviour of the functions in an invariant subspace.

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Authors and Affiliations

  1. Department of Mathematics, Lund University, P.O. Box 118, S-221 00, Lund, Sweden

    Alexandru Aleman

  2. Department of Mathematics, University of Tennessee, 37996-1300, Knoxville, TN, USA

    Stefan Richter & Carl Sundberg

Authors
  1. Alexandru Aleman
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  2. Stefan Richter
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  3. Carl Sundberg
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Corresponding author

Correspondence to Alexandru Aleman.

Additional information

Work of the first author was partially supported by the Royal Swedish Academy of Sciences; work of the second and third authors was supported by the National Science Foundation.

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Aleman, A., Richter, S. & Sundberg, C. The majorization function and the index of invariant sub spaces in the Bergman spaces. J. Anal. Math. 86, 139–182 (2002). https://doi.org/10.1007/BF02786647

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  • DOI: https://doi.org/10.1007/BF02786647

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