Wolff’s theorem on ideals for matrices

Holloway, Caleb; Trent, Tavan

doi:10.1090/S0002-9939-2014-12223-4

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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