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

Studia Mathematica (1992)

- Volume: 103, Issue: 3, page 275-281
- ISSN: 0039-3223

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topMortini, Raymond. "An example of a subalgebra of $H^{∞}$ on the unit disk whose stable rank is not finite." Studia Mathematica 103.3 (1992): 275-281. <http://eudml.org/doc/215950>.

@article{Mortini1992,

abstract = {We present an example of a subalgebra with infinite stable rank in the algebra of all bounded analytic functions in the unit disk.},

author = {Mortini, Raymond},

journal = {Studia Mathematica},

keywords = {subalgebra with infinite stable rank in the algebra of all bounded analytic functions in the unit disk},

language = {eng},

number = {3},

pages = {275-281},

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

url = {http://eudml.org/doc/215950},

volume = {103},

year = {1992},

}

TY - JOUR

AU - Mortini, Raymond

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

JO - Studia Mathematica

PY - 1992

VL - 103

IS - 3

SP - 275

EP - 281

AB - We present an example of a subalgebra with infinite stable rank in the algebra of all bounded analytic functions in the unit disk.

LA - eng

KW - subalgebra with infinite stable rank in the algebra of all bounded analytic functions in the unit disk

UR - http://eudml.org/doc/215950

ER -

## References

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

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