The Michigan Mathematical Journal

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

Raymond Mortini and Brett Wick

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

First available in Project Euclid: 11 August 2010

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Mathematical Reviews number (MathSciNet)

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


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.

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  • 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.