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The common range of co-analytic Toeplitz operators on the Drury-Arveson space

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Abstract

We characterize the common range of the adjoints of cyclic multiplication operators on the Drury-Arveson space. We show that a function belongs to this common range if and only if its Taylor coefficients satisfy a simple decay condition. To achieve this, we introduce the uniform Smirnov class on the ball and determine its dual space. We show that the dual space of the uniform Smirnov class equals the dual space of the strictly smaller Smirnov class of the Drury-Arveson space, and that this in turn equals the common range of the adjoints of cyclic multiplication operators.

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Authors and Affiliations

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

    Alexandru Aleman

  2. Fachrichtung Mathematik, Universität des Saarlandes, 66123, Saarbrücken, Germany

    Michael Hartz

  3. Department of Mathematics, Washington University in St. Louis, One Brookings Drive, St. Louis, MO, 63130, USA

    John E. McCarthy

  4. Department of Mathematics, University of Tennessee, 1403 Circle Drive, Knoxville, TN, 37996-1320, USA

    Stefan Richter

Authors
  1. Alexandru Aleman
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  2. Michael Hartz
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  3. John E. McCarthy
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  4. Stefan Richter
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Corresponding author

Correspondence to John E. McCarthy.

Additional information

M.H. was partially supported by a GIF grant.

J.M. was partially supported by National Science Foundation Grant DMS 2054199.

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Aleman, A., Hartz, M., McCarthy, J.E. et al. The common range of co-analytic Toeplitz operators on the Drury-Arveson space. JAMA 150, 215–247 (2023). https://doi.org/10.1007/s11854-022-0265-9

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  • DOI: https://doi.org/10.1007/s11854-022-0265-9

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