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An Example on Composite Differentiable Functions in Infinite Dimensions

Jaramillo Aguado, Jesús Ángel (1989) An Example on Composite Differentiable Functions in Infinite Dimensions. Bulletin of the Australian Mathematical Society, 40 (1). pp. 91-95. ISSN 0004-9727

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Official URL: http://journals.cambridge.org/abstract_S000497270000352X

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Abstract

We present an example showing that a classical result due to Glaeser about the closedness of composition subalgebras of infinitely differeuniable functions cannot be extended to the case of weakly uniformly differentiable functions on Banach spaces

Item Type:Article
Uncontrolled Keywords:Weakly uniformly differentiable functions; Glaeser theorem; real-analytic mapping; Fréchet topology of uniform convergence on compact subsets of functions and all their derivatives
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16854
References:

R. Aron, J. G6mez and J. Llavona, 'Homomorphisms between algebras of differentiable functions in infinite dimensions', Mich. Math. J. 35 (1988), 163-178.

R. Aron and J. Prolla, 'Polynomial approximations of differentiable functions on Banach spaces', J. Reine Angew. Math. 313 (1980), 195-216.

G. Glaeser, 'Fonctions composees differentiables', Ann. of Math. 77 (1963), 193-209.

H.H. Keller, Differential Calculus in Locally Convex Spaces, Lecture Notes in Math 417 (Sptinger-Verlag, Berlin, Heidelberg, New York, Tokyo, 1974).

J. Llavona, Approximation of Continuously Differentiable Functions, North Holland Math. Studies 130, 1986.

S. Yamamuro, Differential Calculus in Topological Linear Spaces, Lecture Notes in Math. 374 (Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1974).

Deposited On:24 Oct 2012 08:19
Last Modified:07 Feb 2014 09:37

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