# Fréchet algebras and formal power series

Studia Mathematica (1996)

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

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topAllan, 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

top- [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] G. R. Allan, Elements of finite closed descent in a Banach algebra, J. London Math. Soc. (2) 7 (1973), 462-466. Zbl0274.46040
- [3] G. R. Allan, A remark in automatic continuity theory, Bull. London Math. Soc. 12 (1980), 452-454. Zbl0462.46034
- [4] R. F. Arens, Linear topological division algebras, Bull. Amer. Math. Soc. 53 (1947), 632-630.
- [5] R. F. Arens, A generalization of normed rings, Pacific J. Math. 2 (1952), 455-471. Zbl0047.35802
- [6] R. F. Arens, Dense inverse limit rings, Michigan Math. J. 5 (1958), 169-182. Zbl0087.31802
- [7] H. Cartan, Théorie élémentaire des fonctions analytiques d'une ou plusieurs variables complexes, Hermann, Paris, 1963. Zbl0114.03702
- [8] H. G. Dales, Automatic continuity: a survey, Bull. London Math. Soc. 10 (1978), 129-183. Zbl0391.46037
- [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] 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] E. A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1953; third printing 1971). Zbl0047.35502

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