Dense morphisms in commutative Banach algebras
HTML articles powered by AMS MathViewer
- by Gustavo Corach and Fernando Daniel Suárez PDF
- Trans. Amer. Math. Soc. 304 (1987), 537-547 Request permission
Abstract:
Using a new notion of stability we compute exactly the stable rank of the polydisc algebra, extend Oka’s extension theorem to $n$-tuples of functions without common zeros and give an estimation for a question raised by Swan concerning the stable rank of a dense subalgebra of a given Banach algebra.References
- Aldo Andreotti and Raghavan Narasimhan, A topological property of Runge pairs, Ann. of Math. (2) 76 (1962), 499–509. MR 140714, DOI 10.2307/1970370
- H. Bass, $K$-theory and stable algebra, Inst. Hautes Études Sci. Publ. Math. 22 (1964), 5–60. MR 174604
- Henri Cartan, Sur les matrices holomorphes de $n$ variables complexes, J. Math. Pures Appl. 19 (1940), 1–26 (French). MR 0001874
- Gustavo Corach and Angel R. Larotonda, Stable range in Banach algebras, J. Pure Appl. Algebra 32 (1984), no. 3, 289–300. MR 745359, DOI 10.1016/0022-4049(84)90093-8
- Gustavo Corach and Angel R. Larotonda, A stabilization theorem for Banach algebras, J. Algebra 101 (1986), no. 2, 433–449. MR 847169, DOI 10.1016/0021-8693(86)90203-6
- Gustavo Corach and Angel R. Larotonda, Unimodular matrices in Banach algebra theory, Proc. Amer. Math. Soc. 96 (1986), no. 3, 473–477. MR 822443, DOI 10.1090/S0002-9939-1986-0822443-7
- 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, 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, Extension of characters in commutative Banach algebras, Studia Math. 85 (1987), no. 2, 199–202. MR 887321, DOI 10.4064/sm-85-2-199-202 —, Generalized rational convexity in Banach algebras (preprint).
- Th. Duchamp and E. L. Stout, Maximum modulus sets, Ann. Inst. Fourier (Grenoble) 31 (1981), no. 3, v, 37–69 (English, with French summary). MR 638616 T. W. Gamelin, Uniform algebras, Chelsea, New York, 1984.
- Richard H. Herman and Leonid N. Vaserstein, The stable range of $C^{\ast }$-algebras, Invent. Math. 77 (1984), no. 3, 553–555. MR 759256, DOI 10.1007/BF01388839
- Sze-tsen Hu, Homotopy theory, Pure and Applied Mathematics, Vol. VIII, Academic Press, New York-London, 1959. MR 0106454
- 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
- V. Ja. Lin, Holomorphic fiberings and multivalued functions of elements of a Banach algebra, Funkcional. Anal. i Priložen. 7 (1973), no. 2, 43–51 (Russian). MR 0318898
- Ernest Michael, Convex structures and continuous selections, Canadian J. Math. 11 (1959), 556–575. MR 109344, DOI 10.4153/CJM-1959-051-9
- Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101
- Marc A. Rieffel, Dimension and stable rank in the $K$-theory of $C^{\ast }$-algebras, Proc. London Math. Soc. (3) 46 (1983), no. 2, 301–333. MR 693043, DOI 10.1112/plms/s3-46.2.301
- N. Sibony and J. Wermer, Generators for $A(\Omega )$, Trans. Amer. Math. Soc. 194 (1974), 103–114. MR 419838, DOI 10.1090/S0002-9947-1974-0419838-9
- Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
- Edgar Lee Stout, The theory of uniform algebras, Bogden & Quigley, Inc., Publishers, Tarrytown-on-Hudson, N.Y., 1971. MR 0423083
- Richard G. Swan, Topological examples of projective modules, Trans. Amer. Math. Soc. 230 (1977), 201–234. MR 448350, DOI 10.1090/S0002-9947-1977-0448350-9
- Joseph L. Taylor, Topological invariants of the maximal ideal space of a Banach algebra, Advances in Math. 19 (1976), no. 2, 149–206. MR 410384, DOI 10.1016/0001-8708(76)90061-X
- L. N. Vaseršteĭn, The stable range of rings and the dimension of topological spaces, Funkcional. Anal. i Priložen. 5 (1971), no. 2, 17–27 (Russian). MR 0284476
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 304 (1987), 537-547
- MSC: Primary 46J15; Secondary 19K99, 32E25
- DOI: https://doi.org/10.1090/S0002-9947-1987-0911084-4
- MathSciNet review: 911084