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Spaces of differentiable functions with the approximation property. (Spanish: Espacios de funciones diferenciables con la propiedad de aproximación).

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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


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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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