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1996 | 121 | 3 | 277-308
Tytuł artykułu

Stable inverse-limit sequences, with application to Predict algebras

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EN
Abstrakty
EN
The notion of a stable inverse-limit sequence is introduced. It provides a sufficient (and, for sequences of abelian groups, necessary) condition for the preservation of exactness by the inverse-limit functor. Examples of stable sequences are provided through the abstract Mittag-Leffler theorem; the results are applied in the theory of Fréchet algebras.
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Twórcy
  • Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, U.K., G.R.Allan@pmms.cam.ac.uk
Bibliografia
  • [1] G. R. Allan, Embedding the algebra of formal power series in a Banach algebra, Proc. London Math. Soc. (3) 25 (1972), 329-340.
  • [2] G. R. Allan, Fréchet algebras and formal power series, Studia Math. 119 (1996), 271-288.
  • [3] R. F. Arens, A generalization of normed rings, Pacific J. Math. 2 (1952), 455-471.
  • [4] R. F. Arens, Dense inverse limit rings, Michigan Math. J. 5 (1958), 169-182.
  • [5] N. Bourbaki, Théorie des ensembles, Hermann, Paris, 1970.
  • [6] A. M. Davie, Homotopy in Fréchet algebras, Proc. London Math. Soc. (3) 23 (1971), 31-52.
  • [7] S. Eilenberg and N. E. Steenrod, Foundations of Algebraic Topology, Princeton Univ. Press, Princeton, N.J., 1952.
  • [8] R. Engelking, General Topology, revised and completed edition, Heldermann, Berlin, 1989.
  • [9] J. Eschmeier and M. Putinar, Spectral Decompositions and Analytic Sheaves, London Math. Soc. Monographs (N.S.) 10, Clarendon Press, Oxford, 1996.
  • [10] J. Esterle, Mittag-Leffler methods in the theory of Banach algebras and a new approach to Michael's problem, in: Contemp. Math. 32, Amer. Math. Soc., 1984, 107-129.
  • [11] T. W. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs, 1969.
  • [12] R. Godement, Topologie algébrique et théorie des faisceaux, Publ. Inst. Math. Univ. Strasbourg XIII, Hermann, Paris, 1964.
  • [13] G. Köthe, Topological Vector Spaces I, Springer, Berlin, 1969.
  • [14] W. S. Massey, Homology and Cohomology Theory, Marcel Dekker, Basel, 1978.
  • [15] E. A. Michael, Locally multiplicatively convex topological algebras, Mem. Amer. Math. Soc. 11 (1953; third printing 1971).
  • [16] J. Milnor, On axiomatic homology theory, Pacific J. Math. 12 (1962), 337-341.
  • [17] R. Narasimhan, Complex Analysis in One Variable, Birkhäuser, Boston, 1985.
  • [18] V. P. Palomodov, Homological methods in the theory of locally convex spaces, Uspekhi Mat. Nauk 26 (1) (1971), 3-65 (in Russian); English transl.: Russian Math. Surveys 26 (1971), 1-64.
  • [19] J. L. Taylor, A joint spectrum for several commuting operators, J. Funct. Anal. 6 (1970), 172-191.
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Bibliografia
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