Open Access
2010 Stabilization in $H^\infty_{\mathbb{R}}(\mathbb{D})$
Brett D. Wick
Publ. Mat. 54(1): 25-52 (2010).


It is shown that for $H^\infty_\mathbb{R}(\mathbb{D})$ functions $f_1$ and $f_2$ with

$\inf_{z\in\mathbb{D}}(\vert f_1(z)\vert+\vert f_2(z)\vert)\geq\delta>0$

and $f_1$ being positive on the real zeros of $f_2$, then there exists $H^\infty_\mathbb{R}(\mathbb{D})$ functions $g_2$ and $g_1$, $g_1^{-1}$ with norm controlled by a constant depending only on $\delta$ and

$g_1f_1+g_2f_2=1\quad\forall\; z\in\mathbb{D}$.

These results are connected to the computation of the stable rank of the algebra $H^\infty_\mathbb{R}(\mathbb{D})$ and to results in Control Theory.


Download Citation

Brett D. Wick. "Stabilization in $H^\infty_{\mathbb{R}}(\mathbb{D})$." Publ. Mat. 54 (1) 25 - 52, 2010.


Published: 2010
First available in Project Euclid: 8 January 2010

zbMATH: 1193.46033
MathSciNet: MR2603587

Primary: 46E25 , 46J10

Keywords: Banach algebras , control theory , corona Theorem , stable rank

Rights: Copyright © 2010 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.54 • No. 1 • 2010
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