Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1995-1273527-9
MathSciNet review: 1273527
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [Be] M. Behrens, The Corona conjecture for a class of infinitely connected domains, Bull. Amer. Math. Soc. 76 (1970), 387-391. MR 0256166 (41:825)
  • [CoSu] G. Corach and F. D. Suarez, Extension problems and stable rank in commutative Banach algebras, Topology Appl. 21 (1985), 1-8. MR 808718 (87a:46086)
  • [Gam1] T. Gamelin, Uniform algebras, Prentice-Hall, New York, 1969. MR 0410387 (53:14137)
  • [Gam2] -, Localization of corona problem, Pacific J. Math. 34 (1970), 73-81. MR 0276742 (43:2482)
  • [Go] G. M. Golusin, Geometric theory of function of a complex variable, Amer. Math. Soc., Providence, RI, 1969.
  • [Lam] T. Y. Lam, Serre's conjecture, Lecture Notes in Math., vol. 635, Springer-Verlag, Berlin and New York, 1978. MR 0485842 (58:5644)
  • [Ri] M. A. Rieffel, Dimension and stable rank in the K-theory of $ {C^ \ast }$-algebras, Proc. London Math. Soc. (3) 46 (1983), 301-333. MR 693043 (84g:46085)
  • [To1] V. Tolokonnikov, Estimates in the Carleson Corona theorem, ideals of the algebra $ {H^\infty }$, a problem of S.-Nagy, J. Soviet. Math. 22 (1983), 1814-1828.
  • [To2] -, Extension problem to an invertible matrix, Proc. Amer. Math. Soc. 117 (1993), 1023-1030. MR 1123668 (93e:46061)
  • [Tr] S. Treil, Stable rank of $ {H^\infty }$ is equal to one, J. Funct. Anal. 109 (1992), 130-154. MR 1183608 (93h:46076)
  • [Va] L. N. Vaserstein, Stable rank of rings and dimensionality of topological spaces, Functional Anal. Appl. 5 (1971), 102-110. MR 0284476 (44:1701)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46J15, 19B10, 30H05

Retrieve articles in all journals with MSC: 46J15, 19B10, 30H05


Additional Information

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

American Mathematical Society