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A survey on Lipschitz-free Banach Spaces

100%

Godefroy G.

Commentationes Mathematicae

2015

tom 55

nr 2

This article is a survey of Lipschitz\dywiz free Banach spaces and recent progress in the understanding of their structure. The results we present have been obtained in the last fifteen years (and quite often in the last five years). We give a self\dywiz contained presentation of the basic properties of Lipschitz\dywiz free Banach spaces and investigate some specific topics: non-linear transfer of asymptotic smoothness, approximation properties, norm\dywiz attainment. Section 5 consists mainly of unpublished results. A list of open problems with comentary is provided.

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

80%

Deville R., Fonf V., Hájek P.

Studia Mathematica

1996

tom 120

nr 1

61-74

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).

Ograniczanie wyników

1 Commentationes Mathematicae

1 Studia Mathematica

1 Deville R.

1 Fonf V.

1 Godefroy G.

1 Hájek P.

1 2015

1 1996

Wyniki wyszukiwania

A survey on Lipschitz-free Banach Spaces

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