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

• Autorzy: Robert Deville , Vladimir Fonf , Petr Hájek
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

analytic norm   approximation   convex function   geometry of Banach spaces  

Kategorie tematyczne

• 46G20: Infinite-dimensional holomorphy
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 120
• Numer: 1
• Strony: 61-74

Daty

wydano

1996

otrzymano

1995-09-11

poprawiono

1996-01-19

Twórcy

autor

Robert Deville

• Department of Mathematics, Université de Bordeaux, 351, Cours de la Libération, 33400 Talence, France ,

autor

Vladimir Fonf

• Department of Mathematics and Computer Sciences, Ben Gurion University of the Negev, Beer Sheva, Israel ,

autor

Petr Hájek

• Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada ,

Bibliografia

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