The Michigan Mathematical Journal

Spectral characteristics and stable ranks for the Sarason algebra $H^\inf + C$

Raymond Mortini and Brett Wick

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Michigan Math. J. Volume 59, Issue 2 (2010), 395-409.

Dates
First available in Project Euclid: 11 August 2010

Permanent link to this document
http://projecteuclid.org/euclid.mmj/1281531463

Digital Object Identifier
doi:10.1307/mmj/1281531463

Zentralblatt MATH identifier
05792259

Mathematical Reviews number (MathSciNet)
MR2677628

Subjects
Primary: 46J15: Banach algebras of differentiable or analytic functions, Hp-spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30] 30H80: Corona theorems
Secondary: 30H05: Bounded analytic functions

Citation

Mortini, Raymond; Wick, Brett. Spectral characteristics and stable ranks for the Sarason algebra $H^\inf + C$. The Michigan Mathematical Journal 59 (2010), no. 2, 395--409. doi:10.1307/mmj/1281531463. http://projecteuclid.org/euclid.mmj/1281531463.


Export citation

References

  • S. Axler, Factorization of $L^\infty$ functions, Ann. of Math. (2) 106 (1977), 567--572.
  • L. Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. of Math. (2) 76 (1962), 547--559.
  • G. Corach and A. Larotonda, Stable range in Banach algebras, J. Pure Appl. Algebra 32 (1984), 289--300.
  • G. Corach and F. D. Suárez, Stable rank in holomorphic function algebras, Illinois J. Math. 29 (1985), 627--639.
  • ------, On the stable range of uniform algebras and $H^\infty,$ Proc. Amer. Math. Soc. 98 (1986), 607--610.
  • ------, Dense morphisms in commutative Banach algebras, Trans. Amer. Math. Soc. 304 (1987), 537--547.
  • J. B. Garnett, Bounded analytic functions, Pure Appl. Math., 96, Academic Press, New York, 1981.
  • P. Gorkin and R. Mortini, Interpolating Blaschke products and factorization in Douglas algebras, Michigan Math. J. 38 (1991), 147--160.
  • K. Hoffman, Bounded analytic functions and Gleason parts, Ann. of Math. (2) 86 (1967), 74--111.
  • P. W. Jones, D. Marshall, and T. Wolff, Stable rank of the disc algebra, Proc. Amer. Math. Soc. 96 (1986), 603--604.
  • L. Laroco, Stable rank and approximation theorems in $H^\infty,$ Trans. Amer. Math. Soc. 327 (1991), 815--832.
  • R. Mortini and B. D. Wick, The Bass and topological stable ranks of $H_\Bbb R^\infty(\Bbb D)$ and $A_\Bbb R(\Bbb D),$ J. Reine Angew. Math. 636 (2009), 175--191.
  • A. Nicolau and D. Suárez, Approximation by invertible functions in $H^\infty,$ Math. Scand. 99 (2006), 287--319.
  • N. K. Nikolski, Treatise on the shift operator, Grundlehren Math. Wiss., 273, Springer-Verlag, Berlin, 1986.
  • ------, In search of the invisible spectrum, Ann. Inst. Fourier (Grenoble) 49 (1999), 1925--1998.
  • M. Rieffel, Dimension and stable rank in the $K$-theory of $C^*$-algebras, Proc. London Math. Soc. (3) 46 (1983), 301--333.
  • M. Rosenblum, A corona theorem for countably many functions, Integral Equations Operator Theory 3 (1980), 125--137.
  • R. Rupp, Stable ranks of subalgebras of the disc algebra, Proc. Amer. Math. Soc. 108 (1990), 137--142.
  • ------, Stable rank of holomorphic function algebras, Studia Math. 97 (1990), 85--90.
  • ------, Stable rank and the $\bar\partial$-equation, Canad. Math. Bull. 34 (1991), 113--118.
  • ------, Stable rank and boundary principle, Topology Appl. 40 (1991), 307--316.
  • D. Sarason, Algebras of functions on the unit circle, Bull. Amer. Math. Soc. 79 (1973), 286--299.
  • D. Suárez, Cech cohomology and covering dimension for the $H^\infty$ maximal ideal space, J. Funct. Anal. 123 (1994), 233--263.
  • ------, Trivial Gleason parts and the topological stable rank of $H^\infty,$ Amer. J. Math. 118 (1996), 879--904.
  • 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.
  • S. Treil, The stable rank of $H^\infty$ equals 1, J. Funct. Anal. 109 (1992), 130--154.
  • ------, Estimates in the corona theorem and ideals of $H^\infty$: A problem of T. Wolff, J. Anal. Math. 87 (2002), 481--495.
  • S. Treil and B. D. Wick, The matrix-valued $H^p$ corona problem in the disk and polydisk, J. Funct. Anal. 226 (2005), 138--172.
  • T. T. Trent, A new estimate for the vector valued corona problem, J. Funct. Anal. 189 (2002), 267--282.
  • L. Vasershtein, The stable rank of rings and dimensionality of topological spaces, Funktsional Anal. i Prilozhen 5 (1971), 17--27 (Russian); English translation in Funct. Anal. Appl. 5 (1971), 102--110.