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Wolff's theorem on ideals for matrices


Authors: Caleb D. Holloway and Tavan T. Trent
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
Published electronically: October 3, 2014
MathSciNet review: 3283648
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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

DOI: https://doi.org/10.1090/S0002-9939-2014-12223-4
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.