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C-Infinity-Bounding Sets and Compactness

Biström, P. and Jaramillo Aguado, Jesús Ángel (1994) C-Infinity-Bounding Sets and Compactness. Mathematica Scandinavica, 75 (1). pp. 82-86. ISSN 0025-5521

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Abstract

In this article it is proved that any set in a real Banach space on which the C-infinity-functions are bounded, is relatively compact. In particular, for any real Banach space E, a sequence (x(n)) convergences to x in E if and only if f(x(n)) --> S(x) for all f is an element of C-infinity(E).

Item Type:Article
Uncontrolled Keywords:C1-bounding sets; compactness
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16787
Deposited On:22 Oct 2012 10:11
Last Modified:07 Feb 2014 09:35

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