Fréchet algebras and formal power series

Graham R. Allan

ArticleOriginal scientific text

Title

Fréchet algebras and formal power series

Authors ¹

Affiliations

Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, United Kingdom

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.

G. R. Allan, Embedding the algebra of formal power series in a Banach algebra, Proc. London Math. Soc. (3) 25 (1972), 329-340.
G. R. Allan, Elements of finite closed descent in a Banach algebra, J. London Math. Soc. (2) 7 (1973), 462-466.
G. R. Allan, A remark in automatic continuity theory, Bull. London Math. Soc. 12 (1980), 452-454.
R. F. Arens, Linear topological division algebras, Bull. Amer. Math. Soc. 53 (1947), 632-630.
R. F. Arens, A generalization of normed rings, Pacific J. Math. 2 (1952), 455-471.
R. F. Arens, Dense inverse limit rings, Michigan Math. J. 5 (1958), 169-182.
H. Cartan, Théorie élémentaire des fonctions analytiques d'une ou plusieurs variables complexes, Hermann, Paris, 1963.
H. G. Dales, Automatic continuity: a survey, Bull. London Math. Soc. 10 (1978), 129-183.
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.
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.
E. A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1953; third printing 1971).

Title

Fréchet algebras and formal power series

Affiliations

Abstract

Bibliography