## Wolff’s theorem on ideals for matrices

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- by Caleb D. Holloway and Tavan T. Trent
- Proc. Amer. Math. Soc.
**143**(2015), 611-620 - DOI: https://doi.org/10.1090/S0002-9939-2014-12223-4
- Published electronically: October 3, 2014
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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.## References

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## Bibliographic 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