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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Wolff’s theorem on ideals for matrices
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by Caleb D. Holloway and Tavan T. Trent PDF
Proc. Amer. Math. Soc. 143 (2015), 611-620 Request permission

Abstract:

We extend Wolff’s theorem concerning ideals on $H^{\infty }(\mathbb {D})$ to the matrix case, giving conditions under which an $H^{\infty }$-solution $G$ to the equation $FG = H$ exists for all $z \in \mathbb {D}$, where $F$ is an $m \times \infty$ matrix of functions in $H^{\infty }(\mathbb {D})$, and $H$ is an $m \times 1$ vector of such functions. We then examine several useful results.
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Additional Information
  • Caleb D. Holloway
  • Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
  • Email: chollow@uark.edu
  • Tavan T. Trent
  • Affiliation: Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487
  • Email: ttrent@gp.as.ua.edu
  • Received by editor(s): January 25, 2013
  • Received by editor(s) in revised form: April 4, 2013
  • Published electronically: October 3, 2014
  • Communicated by: Pamela B. Gorkin
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 611-620
  • MSC (2010): Primary 30H05, 30H80
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12223-4
  • MathSciNet review: 3283648