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Stable rank of $ H\sp \infty$ in multiply connected domains

Author: V. Tolokonnikov
Journal: Proc. Amer. Math. Soc. 123 (1995), 3151-3156
MSC: Primary 46J15; Secondary 19B10, 30H05
MathSciNet review: 1273527
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Abstract: The stable rank of the algebra $ {H^\infty }(G)$ of bounded analytic functions in every finitely connected open Riemann surface is equal to one. The same is true for some infinitely connected plain domains (Behrens domains). The proof is based on the Treil theorem, which considered the case of $ {H^\infty }$ in the unit disk.

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Keywords: Stable rank, algebra $ {H^\infty }$, Riemann surfaces, homotopy, extension to invertible matrix
Article copyright: © Copyright 1995 American Mathematical Society

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