A note about stabilization in Aℝ(ⅅ)

Brett D. Wick

doi:10.1002/mana.200610779

A note about stabilization in Aℝ(ⅅ)

Brett D. Wick

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

It is shown that for A_{R{double-struck}}(D{double-struck}) functions f₁ and f₂ with and f₁ being positive on real zeros of f₂ then there exists A_{R{double-struck}}(D{double-struck}) functions g₂ and g₁, g^-1₁ with and g₁f₁ + g₂f₂ = 1 for all z ∈ D{double-struck}. This result is connected to the computation of the stable rank of the algebra A_{R{double-struck}}(D{double-struck}) and to Control Theory.

Original language	English
Pages (from-to)	912-916
Number of pages	5
Journal	Mathematische Nachrichten
Volume	282
Issue number	6
DOIs	https://doi.org/10.1002/mana.200610779
State	Published - Jun 2009

Keywords

Banach algebras
Control theory
Corona theorem
Stable rank

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10.1002/mana.200610779

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title = "A note about stabilization in Aℝ(ⅅ)",

abstract = "It is shown that for AR\{double-struck\}(D\{double-struck\}) functions f1 and f2 with and f1 being positive on real zeros of f2 then there exists AR\{double-struck\}(D\{double-struck\}) functions g2 and g1, g-11 with and g1f1 + g2f2 = 1 for all z ∈ D\{double-struck\}. This result is connected to the computation of the stable rank of the algebra AR\{double-struck\}(D\{double-struck\}) and to Control Theory.",

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AB - It is shown that for AR{double-struck}(D{double-struck}) functions f1 and f2 with and f1 being positive on real zeros of f2 then there exists AR{double-struck}(D{double-struck}) functions g2 and g1, g-11 with and g1f1 + g2f2 = 1 for all z ∈ D{double-struck}. This result is connected to the computation of the stable rank of the algebra AR{double-struck}(D{double-struck}) and to Control Theory.

KW - Banach algebras

KW - Control theory

KW - Corona theorem

KW - Stable rank

UR - https://www.scopus.com/pages/publications/67650497258

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DO - 10.1002/mana.200610779

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VL - 282

SP - 912

EP - 916

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 6

ER -

A note about stabilization in Aℝ(ⅅ)

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Keywords

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