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The Corona Theorem and stable rank for the algebra C plus BH infinity

Mortini, Raymond, Sasane, Amol and Wick, Brett (2010) The Corona Theorem and stable rank for the algebra C plus BH infinity. Houston Journal of Mathematics, 36 (1). pp. 289-301. ISSN 0362-1588

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Abstract

Let B be a Blaschke product. We prove in several different ways the Corona theorem for the algebra H∞B:=C+BH∞. That is, we show the equivalence of the classical Corona Condition Σ |fj | > δ> 0 on data f1, …, fn in H∞B and the solvability of the Bezout equation Σ gjfj =1 for g1, …, gn. Estimates on solutions to the Bezout equation are also obtained. We also show that the Bass stable rank of H∞B is 1. Analogous results are obtained also for A(D)B.

Item Type: Article
Official URL: http://www.math.uh.edu/~hjm/
Additional Information: ©2010 The University of Houston
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: UT ISI:000276308000019
Date Deposited: 23 Jul 2010 13:12
URL: http://eprints.lse.ac.uk/28828/

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