RT Journal Article
T1 Spaces of differentiable functions with the approximation property. (Spanish: Espacios de funciones diferenciables con la propiedad de aproximación).
A1 Bombal Gordón, Fernando
AB The author, in a joint paper with J. L. González Llvona [same journal 70 (1976), no. 4, 727–741; proved that a real Banach space E satisfies the approximation property if and only if the space Cnc(E), of n times continuously differentiable real functions, in the sense of Hadamard, on E, endowed with the topology that has the sets T(K,r)={f∈Cnc(E):Dpf(K)(Kp)⊂[−r,r],0≤p≤n} (where K runs over the compact sets of E and r>0) as a base for the neighborhoods of 0, satisfies the approximation property for some (and hence for every) n≥1. The author now proves this result when, instead of Cnc(E), one considers the space of n times continuously differentiable functions with respect to any other notion of differentiation which satisfies reasonable conditions (satisfied in particular by the Fréchet differential).
PB Real Academia de Ciencias Exactas, Físicas y Naturales
SN 0034-0596
YR 1978
FD 1978
LK https://hdl.handle.net/20.500.14352/64744
UL https://hdl.handle.net/20.500.14352/64744
LA spa
NO Aron, R. M. y Schottenloher, M. 1974. Compact holomorphic mappings on Banach spaces and the approximation property. Bull, of the Amer. Math. Soc., vol. 80, num. 6.Bombal, F. y LLAVONA, J. L. G. La propiedad de aproximación en espacios de funciones diferenciables. Rev. Real Acad. Ciencias de Madrid, t. 70, 337-346 (1976).González Llavona, J. L. 1975. Aproximación de funciones diferenciables. Tesis doctoral. Publicaciones de la Facultad de Matemáticas de la Universidad Complutense.Lesmes, J. 1974. On the approximation of continuously differentiable functions in Hilbert spaces. Rev. Colombiana de Matemáticas, vol. Vili, 217-223.Nachbin, L. 1949. Sur les algebres denses de fonctions differentiates sur une variété. C. R. Acad. Sci. Paris, 288, 1549- 1551.Schwartz, L. : 1953/54. Produits tensoriels topologiques d'espaces vectoriels topologiques. Séminaire Schwartz.Yamamuro, S. 1974. Differential calculus in topological linear spaces. Lect. Notes, in Math., num. 374. Springer, Berlin.
DS Docta Complutense
RD 27 abr 2024