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Corach, G.; Larotonda, A.R. "Unimodular matrices in banach algebra theory" (1986) Proceedings of the American Mathematical Society. 96(3):473-477
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Abstract:

Let A be a ring with 1 and denote by L (resp. R) the set of left (resp. right) invertible elements of A. If A has an involution *, there is a natural bijection between L and R. In general, it seems that there is no such bijection; if A is a Banach algebra, L and R are open subsets of A, and they have the same cardinality. More generally, we prove that the spaces Uk(An) of n X k-left-invertible matrices and kU(An) of k X n-right-invertible matrices are homotopically equivalent. As a corollary, we answer negatively two questions of Rieffel. © 1986 American Mathematical Society.

Registro:

Documento: Artículo
Título:Unimodular matrices in banach algebra theory
Autor:Corach, G.; Larotonda, A.R.
Filiación:Instituto Argentino de Matemática, Viamonte 1636, Buenos Aires, 1055, Argentina
Departamento de Matemátics, Facultad de Ciencias Exactas, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Año:1986
Volumen:96
Número:3
Página de inicio:473
Página de fin:477
DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0822443-7
Título revista:Proceedings of the American Mathematical Society
Título revista abreviado:Proc. Am. Math. Soc.
ISSN:00029939
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v96_n3_p473_Corach

Referencias:

  • Bourbaki, N., Varietés, Fascicule de résultats, Hermann (1967) Paris
  • Corach, G., Larotonda, A.R., A Stabilization Theorem for Banach Algebras, , J. Algebra (to appear)
  • Dold, A., Partitions of unity in the theory of fibrations (1963) Ann. Of Math. (2), 78, pp. 223-255
  • Hu, S.T., (1959) Homotopy Theory, , Academic Press, New York
  • Kuiper, N., The homotopy type of the unitary group of Hilbert space (1965) Topology, 3, pp. 19-30
  • Lam, T.Y., Serre's conjecture (1978) Lecture Notes in Math., 635. , Springer-Verlag, Berlin and New York
  • Lang, S., (1972) Differentiable Manifolds, Addison-Wesley, , Reading, Mass
  • Lin, V.Y., Holomorphic fibering and multivalued functions of elements of a Banach algebra (1973) Funct. Anal, 7, pp. 122-128
  • Novodvorski, M.E., Certain homotopical invariants of spaces of maximal ideals, Mat (1967) Zametki, pp. 487-494
  • Palais, R.S., Homotopy theory of infinite dimensional manifolds (1966) Topology, 5, pp. 1-16
  • Raeburn, I., The relationship between a commutative Banach algebra and its maximal ideal space (1978) J. Funct. Anal, 25, pp. 366-390
  • Rieffel, M., Dimension and stable rank in the K-theory of C*-algebras, Proc. London (1983) Math. Soc. (3), 46, pp. 301-333
  • Swam, R., (1962) Vector Bundles and Projective Bundles, 105, pp. 264-277. , Trans. Amer. Math. Soc
  • Taylor, J.L., Topological invariants of the maximal ideal space of a Banach algebra (1976) Adv. In Math., 19, pp. 149-206

Citas:

---------- APA ----------
Corach, G. & Larotonda, A.R. (1986) . Unimodular matrices in banach algebra theory. Proceedings of the American Mathematical Society, 96(3), 473-477.
http://dx.doi.org/10.1090/S0002-9939-1986-0822443-7
---------- CHICAGO ----------
Corach, G., Larotonda, A.R. "Unimodular matrices in banach algebra theory" . Proceedings of the American Mathematical Society 96, no. 3 (1986) : 473-477.
http://dx.doi.org/10.1090/S0002-9939-1986-0822443-7
---------- MLA ----------
Corach, G., Larotonda, A.R. "Unimodular matrices in banach algebra theory" . Proceedings of the American Mathematical Society, vol. 96, no. 3, 1986, pp. 473-477.
http://dx.doi.org/10.1090/S0002-9939-1986-0822443-7
---------- VANCOUVER ----------
Corach, G., Larotonda, A.R. Unimodular matrices in banach algebra theory. Proc. Am. Math. Soc. 1986;96(3):473-477.
http://dx.doi.org/10.1090/S0002-9939-1986-0822443-7