Stable rank of subalgebras of the disc algebra

Rupp, Rudolf

doi:10.1090/S0002-9939-1990-0994789-4

Stable rank of subalgebras of the disc algebra
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Proc. Amer. Math. Soc. 108 (1990), 137-142 Request permission

Abstract:

We calculate the stable rank of subalgebras (in the algebraic sense) of the disc algebra. We extend the results to subalgebras of $A(\bar G)$, where $G$ is a bounded domain whose boundary consists of finitely many closed nonintersecting Jordan curves.

References

H. Bass, $K$-theory and stable algebra, Inst. Hautes Études Sci. Publ. Math. 22 (1964), 5–60. MR 174604
Gustavo Corach and Fernando Daniel Suárez, Extension problems and stable rank in commutative Banach algebras, Topology Appl. 21 (1985), no. 1, 1–8. MR 808718, DOI 10.1016/0166-8641(85)90052-5
Gustavo Corach and Fernando Daniel Suárez, Stable rank in holomorphic function algebras, Illinois J. Math. 29 (1985), no. 4, 627–639. MR 806470
Gustavo Corach and Fernando Daniel Suárez, On the stable range of uniform algebras and $H^\infty$, Proc. Amer. Math. Soc. 98 (1986), no. 4, 607–610. MR 861760, DOI 10.1090/S0002-9939-1986-0861760-1
Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
G. M. Golusin, Geometrische Funktionentheorie, Hochschulbücher für Mathematik, Band 31, VEB Deutscher Verlag der Wissenschaften, Berlin, 1957 (German). MR 0089896
Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
P. W. Jones, D. Marshall, and T. Wolff, Stable rank of the disc algebra, Proc. Amer. Math. Soc. 96 (1986), no. 4, 603–604. MR 826488, DOI 10.1090/S0002-9939-1986-0826488-2

Über den Bass-Stable-Rank komplexer Funktionen-Algebren

Stable rank of holomorphic function algebras

W. P. Novinger, Holomorphic functions with infinitely differentiable boundary values, Illinois J. Math. 15 (1971), 80–90. MR 269861