The Corona Theorem and Stable Rank for the algebra C +BH^infinity

• Autores: Raymond Mortini, Amol Sasane, Brett D. Wick
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 36, Nº 1, 2010, págs. 289-302
• Idioma: inglés
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• Resumen

  • 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 ? |fj | > ?> 0 on data f1, �, fn in H?B and the solvability of the Bezout equation ? 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.