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Bombal Gordón, Fernando
(1978)
*Spaces of differentiable functions with the approximation property. (Spanish: Espacios de funciones diferenciables con la propiedad de aproximación).*
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales de Madrid, 72
(3).
pp. 453-458.
ISSN 0034-0596

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Official URL: http://www.rac.es/4/4_7_1.php?pid=Revistas:REV_20091030_00328&pageNum=0

## Abstract

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).

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Banach spaces; convex spaces |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 17955 |

Deposited On: | 25 Jan 2013 09:48 |

Last Modified: | 07 Aug 2018 10:32 |

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