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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1273527-9
PII: S 0002-9939(1995)1273527-9
Keywords: Stable rank, algebra $ {H^\infty }$, Riemann surfaces, homotopy, extension to invertible matrix
Article copyright: © Copyright 1995 American Mathematical Society