Smooth approximations of norms in separable Banach spaces

2011/05/30 by Petr Hájek, Hájek, Petr, Jarno Talponen +1
Mathematics · #46T20 #47J07 #Algebraic Geometry (math.AG) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B03 #math.AG #math.FA #msc:46B03 #msc:46T20 #msc:47J07

paper · pdf · doi:10.48550/arxiv.1105.6046

9 pages

arxiv created 2012/08/21 · arxiv updated 2012/08/22

Abstract

Let X be a separable real Banach space having a k-times continuously Fréchet differentiable (i.e. C^k-smooth) norm where k=1,...,∞. We show that any equivalent norm on X can be approximated uniformly on bounded sets by C^k-smooth norms.

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