Extension of local smooth maps of Banach spaces

2017/03/18 by Genrich Belitskii, Belitskii, Genrich, Victoria Rayskin +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1703.06299

arxiv created 2017/03/18 · arxiv updated 2017/03/21

Abstract

It is known that smooth bump functions are absent in the majority of infinite-dimensional Banach spaces. This is an obstacle in the development of local analysis, in particular in the questions of extending local maps onto the whole space. We suggest an approach that substitutes bump functions with special maps, which we call K-maps. It allows us to extend smooth local maps from non-smooth spaces, such as C^q[0,1], q=0,1,.... We also prove the Borel lemma for spaces possessing K-maps.

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