## Abstract

We prove that in separable Hilbert spaces, in ℓp(Nℕ) for p an even integer, and in Lp[0,1] for p an even integer, every equivalent norm can be approximated uniformly on bounded sets by analytic norms. In ℓp(Nℕ) and in Lp[0,1] for p ∉ Nℕ (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).

Original language | English |
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Pages (from-to) | 61-74 |

Number of pages | 14 |

Journal | Studia Mathematica |

Volume | 120 |

Issue number | 1 |

State | Published - 1 Dec 1996 |

## Keywords

- Analytic norm
- Approximation
- Convex function
- Geometry of Banach spaces

## ASJC Scopus subject areas

- General Mathematics

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