Geodesic
Analytic and $C^k$ approximations of norms in separable Banach spaces
Studia Mathematica, Tome 120 (1996) no. 1, pp. 61-74

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We prove that in separable Hilbert spaces, in $ℓ_{p}(ℕ)$ for p an even integer, and in $L_{p}[0,1]$ for p an even integer, every equivalent norm can be approximated uniformly on bounded sets by analytic norms. In $ℓ_{p}(ℕ)$ and in $L_{p}[0,1]$ for p ∉ ℕ (resp. for p an odd integer), every equivalent norm can be approximated uniformly on bounded sets by $C^[p]}$-smooth norms (resp. by $C^{p-1}$-smooth norms).
DOI : 10.4064/sm-120-1-61-74
Keywords: analytic norm, approximation, convex function, geometry of Banach spaces

Robert Deville 1 ;  1 ;  1

1 
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Robert Deville;  ;  . Analytic and $C^k$ approximations of norms in separable Banach spaces. Studia Mathematica, Tome 120 (1996) no. 1, pp. 61-74. doi: 10.4064/sm-120-1-61-74

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