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Title

Stable inverse-limit sequences, with application to Predict algebras

Authors 1

Affiliations

  1. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, U.K.

Abstract

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.

Bibliography

  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.
Studia Mathematica
1996/121/3
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Pages:
277-308
Main language of publication
English
Received
1996-05-13
Accepted
1996-08-06
Published
1996
Exact and natural sciences