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

• Autorzy: Raymond Mortini
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 46J15: Banach algebras of differentiable or analytic functions, H p -spaces
• 19B10: Stable range conditions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1992
• Tom: 103
• Numer: 3
• Strony: 275-281

Daty

wydano

1992

otrzymano

1992-02-26

poprawiono

1992-06-15

Twórcy

autor

Raymond Mortini

• Mathematisches Institut I, Universität Karlsruhe, Postfach 6980, D-7500 Karlsruhe 1, Germany

Bibliografia

• [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.
• [3] G. Corach and A. R. Larotonda, Stable range in Banach algebras, J. Pure Appl. Algebra 32 (1984), 289-300.
• [4] G. Corach and F. Suárez, Extension problems and stable rank in commutative Banach algebras, Topology Appl. 21 (1985), 1-8.
• [5] G. Corach and F. Suárez, Stable rank in holomorphic function algebras, Illinois J. Math. 29 (1985), 627-639.
• [6] G. Corach and F. Suárez, Dense morphisms in commutative Banach algebras, Trans. Amer. Math. Soc. 304 (1987), 537-547.
• [7] T. W. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs, N.J., 1969.
• [8] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York 1981.
• [9] P. Jones, D. Marshall and T. H. Wolff, Stable rank of the disc algebra, Proc. Amer. Math. Soc. 96 (1986), 603-604.
• [10] L. Laroco, Stable rank and approximation theorems in $H^∞$, Trans. Amer. Math. Soc. 327 (1991), 815-832.
• [11] R. Rupp, Stable rank of subalgebras of the disk algebra, Proc. Amer. Math. Soc. 108 (1990), 137-142.
• [12] R. Rupp, Stable rank of subalgebras of the ball algebra, ibid. 109 (1990), 781-786.
• [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 $H^∞$ is one, preprint.
• [15] L. N. Vaserstein, Stable rank of rings and dimensionality of topological spaces, Funct. Anal. Appl. 5 (1971), 102-110.