Stable elements of Banach and Fréchet algebras

• Autorzy: Graham R. Allan
• Języki publikacji: EN

Abstrakty

EN

We introduce an algebraic notion-stability-for an element of a commutative ring. It is shown that the stable elements of Banach algebras, and of Fréchet algebras, may be simply described. Part of the theory of power-series embeddings, given in [1] and [4], is seen to be of a purely algebraic nature. This approach leads to other natural questions.

Kategorie tematyczne

• 46M20: Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
• 46J10: Banach algebras of continuous functions, function algebras
• 46M40: Inductive and projective limits
• 46M15: Categories, functors

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 129
• Numer: 1
• Strony: 67-96

Daty

wydano

1998

otrzymano

1997-11-20

Twórcy

autor

Graham R. Allan

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

Bibliografia

• [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, Elements of finite closed descent in a Banach algebra, J. London Math. Soc. (2) 7 (1973), 462-466.
• [3] G. R. Allan, Ideals of rapidly growing functions, in: Proc. Internat. Sympos. on Functional Analysis and its Applications, Univ. of Ibadan, 1977, 85-109.
• [4] G. R. Allan, Fréchet algebras and formal power series, Studia Math. 119 (1996), 271-288.
• [5] G. R. Allan, Stable inverse-limit sequences, with application to Fréchet algebras, ibid. 121 (1996), 277-308.
• [6] R. F. Arens, Linear topological division algebras, Bull. Amer. Math. Soc. 53 (1947), 632-630.
• [7] R. F. Arens, A generalization of normed rings, Pacific J. Math. 2 (1952), 455-471.
• [8] H. G. Dales, Automatic continuity: a survey, Bull. London Math. Soc. 10 (1978), 129-183.
• [9] S. Eilenberg and N. E. Steenrod, Foundations of Algebraic Topology, Princeton Univ. Press, Princeton, N.J., 1952.
• [10] E. A. Michael, Locally multiplicatively convex topological algebras, Mem. Amer. Math. Soc. 11 (1953; third printing 1971).
• [11] O. Zariski and P. Samuel, Commutative Algebra, Vol. II, Van Nostrand, Princeton, 1960.