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A Note about Stabilization in $A_\R(\D)$

By Brett D. Wick

Abstract

It is shown that for $A_\R(\D)$ functions $f_1$ and $f_2$ with $$ \inf_{z\in\bar{\D}}(\abs{f_1(z)}+\abs{f_2(z)})\geq\delta>0 $$ and $f_1$ being positive on real zeros of $f_2$ then there exists $A_\R(\D)$ functions $g_2$ and $g_1,g_1^{-1}$ with and $$ g_1f_1+g_2f_2=1\quad\forall z\in\bar{\D}. $$ This result is connected to the computation of the stable rank of the algebra $A_\R(\D)$ and to Control Theory.Comment: 5 pages, to appear in Math. Nach

Topics: Mathematics - Classical Analysis and ODEs, Mathematics - Complex Variables, Primary 46E25, 46J10
Publisher: 'Wiley'
Year: 2007
DOI identifier: 10.1002/mana.200610779
OAI identifier: oai:arXiv.org:math/0702003

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