An example of a subalgebra of $H^{\infty }$ on the unit disk whose stable rank is not finite

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1. [1] H. Bass, K-theory and stable algebra, IHES Publ. Math. 22 (1964), 5-60. 
2. [2] B. J. Cole and T. W. Gamelin, Representing measures and Hardy spaces for the infinite polydisk algebra, Proc. London Math. Soc. 53 (1986), 112-142. Zbl0624.46032
3. [3] G. Corach and A. R. Larotonda, Stable range in Banach algebras, J. Pure Appl. Algebra 32 (1984), 289-300. Zbl0571.46032
4. [4] G. Corach and F. Suárez, Extension problems and stable rank in commutative Banach algebras, Topology Appl. 21 (1985), 1-8. Zbl0606.46033
5. [5] G. Corach and F. Suárez, Stable rank in holomorphic function algebras, Illinois J. Math. 29 (1985), 627-639. Zbl0606.46034
6. [6] G. Corach and F. Suárez, Dense morphisms in commutative Banach algebras, Trans. Amer. Math. Soc. 304 (1987), 537-547. Zbl0633.46054
7. [7] T. W. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs, N.J., 1969. Zbl0213.40401
8. [8] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York 1981. Zbl0469.30024
9. [9] P. Jones, D. Marshall and T. H. Wolff, Stable rank of the disc algebra, Proc. Amer. Math. Soc. 96 (1986), 603-604. Zbl0626.46043
10. [10] L. Laroco, Stable rank and approximation theorems in $H^{\infty }$, Trans. Amer. Math. Soc. 327 (1991), 815-832. Zbl0744.46040
11. [11] R. Rupp, Stable rank of subalgebras of the disk algebra, Proc. Amer. Math. Soc. 108 (1990), 137-142. Zbl0697.46021
12. [12] R. Rupp, Stable rank of subalgebras of the ball algebra, ibid. 109 (1990), 781-786. Zbl0729.46024
13. [13] S. Scheinberg, Cluster sets and corona theorems, in: Lecture Notes in Math. 604, Springer 1977, 103-106. 
14. [14] S. Treil, The stable rank of the algebra $H^{\infty }$ is one, preprint. Zbl0784.46037
15. [15] L. N. Vaserstein, Stable rank of rings and dimensionality of topological spaces, Funct. Anal. Appl. 5 (1971), 102-110. Zbl0239.16028