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Article Dans Une Revue Mediterranean Journal of Mathematics Année : 2018

Extremal Structure and Duality of Lipschitz Free Spaces

Résumé

We analyse the relationship between different extremal notions in Lipschitz free spaces (strongly exposed, exposed, preserved extreme and extreme points). We prove in particular that every preserved extreme point of the unit ball is also a denting point. We also show in some particular cases that every extreme point is a molecule, and that a molecule is extreme whenever the two points, say x and y, which define it satisfy that the metric segment [x, y] only contains x and y. The most notable among them is the case when the free space admits an isometric predual with some additional properties. As an application, we get some new consequences about norm attainment in spaces of vector-valued Lipschitz functions.
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Dates et versions

hal-02373898 , version 1 (21-11-2019)

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Luis García-Lirola, Colin Petitjean, Antonin . Prochazka, Abraham Rueda Zoca. Extremal Structure and Duality of Lipschitz Free Spaces. Mediterranean Journal of Mathematics, 2018, 15 (2), pp.69. ⟨10.1007/s00009-018-1113-0⟩. ⟨hal-02373898⟩
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