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An Example on Composite Differentiable Functions in Infinite Dimensions

Impacto

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




Resumen

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


Tipo de documento:Artículo
Palabras clave:Weakly uniformly differentiable functions; Glaeser theorem; real-analytic mapping; Fréchet topology of uniform convergence on compact subsets of functions and all their derivatives
Materias:Ciencias > Matemáticas > Análisis funcional y teoría de operadores
Código ID:16854
Referencias:

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).

Depositado:24 Oct 2012 08:19
Última Modificación:07 Feb 2014 09:37

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