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
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.
|Additional Information:||©2010 The University of Houston|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
|Identification Number:||UT ISI:000276308000019|
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