Fréchet algebras and formal power series

Graham Allan

Studia Mathematica (1996)

  • Volume: 119, Issue: 3, page 271-288
  • ISSN: 0039-3223

Abstract

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The class of elements of locally finite closed descent in a commutative Fréchet algebra is introduced. Using this notion, those commutative Fréchet algebras in which the algebra ℂ[[X]] may be embedded are completely characterized, and some applications to the theory of automatic continuity are given.

How to cite

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Allan, Graham. "Fréchet algebras and formal power series." Studia Mathematica 119.3 (1996): 271-288. <http://eudml.org/doc/216300>.

@article{Allan1996,
abstract = {The class of elements of locally finite closed descent in a commutative Fréchet algebra is introduced. Using this notion, those commutative Fréchet algebras in which the algebra ℂ[[X]] may be embedded are completely characterized, and some applications to the theory of automatic continuity are given.},
author = {Allan, Graham},
journal = {Studia Mathematica},
keywords = {elements of locally finite closed descent; commutative Fréchet algebra; automatic continuity},
language = {eng},
number = {3},
pages = {271-288},
title = {Fréchet algebras and formal power series},
url = {http://eudml.org/doc/216300},
volume = {119},
year = {1996},
}

TY - JOUR
AU - Allan, Graham
TI - Fréchet algebras and formal power series
JO - Studia Mathematica
PY - 1996
VL - 119
IS - 3
SP - 271
EP - 288
AB - The class of elements of locally finite closed descent in a commutative Fréchet algebra is introduced. Using this notion, those commutative Fréchet algebras in which the algebra ℂ[[X]] may be embedded are completely characterized, and some applications to the theory of automatic continuity are given.
LA - eng
KW - elements of locally finite closed descent; commutative Fréchet algebra; automatic continuity
UR - http://eudml.org/doc/216300
ER -

References

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  1. [1] G. R. Allan, Embedding the algebra of formal power series in a Banach algebra, Proc. London Math. Soc. (3) 25 (1972), 329-340. Zbl0243.46059
  2. [2] G. R. Allan, Elements of finite closed descent in a Banach algebra, J. London Math. Soc. (2) 7 (1973), 462-466. Zbl0274.46040
  3. [3] G. R. Allan, A remark in automatic continuity theory, Bull. London Math. Soc. 12 (1980), 452-454. Zbl0462.46034
  4. [4] R. F. Arens, Linear topological division algebras, Bull. Amer. Math. Soc. 53 (1947), 632-630. 
  5. [5] R. F. Arens, A generalization of normed rings, Pacific J. Math. 2 (1952), 455-471. Zbl0047.35802
  6. [6] R. F. Arens, Dense inverse limit rings, Michigan Math. J. 5 (1958), 169-182. Zbl0087.31802
  7. [7] H. Cartan, Théorie élémentaire des fonctions analytiques d'une ou plusieurs variables complexes, Hermann, Paris, 1963. Zbl0114.03702
  8. [8] H. G. Dales, Automatic continuity: a survey, Bull. London Math. Soc. 10 (1978), 129-183. Zbl0391.46037
  9. [9] J. Esterle, Elements for a classification of commutative radical Banach algebras, in: Radical Banach Algebras and Automatic Continuity, J. Bachar et al. (eds.), Lecture Notes in Math. 975, Springer, 1983, 4-65. 
  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] E. A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1953; third printing 1971). Zbl0047.35502

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