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The corona theorem and stable rank for the algebra C + BH∞
Department of Mathematics, University of South Carolina.
2010 (English)In: Houston Journal of Mathematics, ISSN 0362-1588, Vol. 36, no 1, p. 289-302Article in journal (Refereed) Published
Abstract [en]

Let B be a Blaschke product. We prove in several different ways the corona theorem for the algebra HB ∞ := C + BH ∞. That is, we show the equivalence of the classical corona condition on data f1,...,fn ε HB ∞ ∀ z ε D, Σ k=1 n |fk(z)| ≥ δ > 0, and the solvability of the Bezout equation for 91,..., 9nB ∞ ∀ z ε D, Σ k=1 n 9k(z)fk(z) = 1. Estimates on solutions to the Bezout equation are also obtained. We also show that the Bass stable rank of H B ∞ is 1. Let A(D)Bbe the subalgebra of all elements from HB ∞ having a continuous extension to the closed unit disk D̄, Analogous results are obtained also for A(D)B.

Place, publisher, year, edition, pages
2010. Vol. 36, no 1, p. 289-302
Keywords [en]
Bass stable rank, Bezout equation, Blaschke products, Corona theorem, Ideals, Subalgebras of h∞
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-149413ISI: 000276308000019Scopus ID: 2-s2.0-77951873865OAI: oai:DiVA.org:kth-149413DiVA, id: diva2:739441
Note

QC 20140821

Available from: 2014-08-21 Created: 2014-08-21 Last updated: 2017-12-05Bibliographically approved

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