Stable inverse-limit sequences, with application to Predict algebras

Graham Allan

Studia Mathematica (1996)

  • Volume: 121, Issue: 3, page 277-308
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Allan, Graham. "Stable inverse-limit sequences, with application to Predict algebras." Studia Mathematica 121.3 (1996): 277-308. <http://eudml.org/doc/216356>.

@article{Allan1996,
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.},
author = {Allan, Graham},
journal = {Studia Mathematica},
keywords = {stable inverse-limit sequence; preservation of exactness by the inverse-limit functor; abstract Mittag-Leffler theorem; theory of Fréchet algebras},
language = {eng},
number = {3},
pages = {277-308},
title = {Stable inverse-limit sequences, with application to Predict algebras},
url = {http://eudml.org/doc/216356},
volume = {121},
year = {1996},
}

TY - JOUR
AU - Allan, Graham
TI - Stable inverse-limit sequences, with application to Predict algebras
JO - Studia Mathematica
PY - 1996
VL - 121
IS - 3
SP - 277
EP - 308
AB - 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.
LA - eng
KW - stable inverse-limit sequence; preservation of exactness by the inverse-limit functor; abstract Mittag-Leffler theorem; theory of Fréchet algebras
UR - http://eudml.org/doc/216356
ER -

References

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  2. [2] G. R. Allan, Fréchet algebras and formal power series, Studia Math. 119 (1996), 271-288. Zbl0858.46041
  3. [3] R. F. Arens, A generalization of normed rings, Pacific J. Math. 2 (1952), 455-471. Zbl0047.35802
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  10. [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. Zbl0569.46031
  11. [11] T. W. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs, 1969. Zbl0213.40401
  12. [12] R. Godement, Topologie algébrique et théorie des faisceaux, Publ. Inst. Math. Univ. Strasbourg XIII, Hermann, Paris, 1964. Zbl0080.16201
  13. [13] G. Köthe, Topological Vector Spaces I, Springer, Berlin, 1969. Zbl0179.17001
  14. [14] W. S. Massey, Homology and Cohomology Theory, Marcel Dekker, Basel, 1978. 
  15. [15] E. A. Michael, Locally multiplicatively convex topological algebras, Mem. Amer. Math. Soc. 11 (1953; third printing 1971). 
  16. [16] J. Milnor, On axiomatic homology theory, Pacific J. Math. 12 (1962), 337-341. Zbl0114.39604
  17. [17] R. Narasimhan, Complex Analysis in One Variable, Birkhäuser, Boston, 1985. Zbl0561.30001
  18. [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. [19] J. L. Taylor, A joint spectrum for several commuting operators, J. Funct. Anal. 6 (1970), 172-191. Zbl0233.47024

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