A+ CATEGORY SCIENTIFIC UNIT

Analytic and $C^k$ approximations of norms in separable Banach spaces

Volume 120 / 1996

Robert Deville, , Studia Mathematica 120 (1996), 61-74 DOI: 10.4064/sm-120-1-61-74

Abstract

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).

Authors

  • Robert Deville


Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image