Extreme points of the unit ball of the space of Lipschitz functions

Farmer, Jeff D.

doi:10.1090/S0002-9939-1994-1195718-7

Extreme points of the unit ball of the space of Lipschitz functions

Author: Jeff D. Farmer
Journal: Proc. Amer. Math. Soc. 121 (1994), 807-813
MSC: Primary 46E15; Secondary 46B20
DOI: https://doi.org/10.1090/S0002-9939-1994-1195718-7
MathSciNet review: 1195718
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Abstract: We consider the space of all Lipschitz functions on a metric space with bounded Lipschitz norm, and give an intrinsic characterization of the extreme points of the unit ball. We briefly discuss some examples of extreme Lipschitz functions, and apply the result to show that if the norm of a Banach space is Gateaux differentiable then extreme functions on any one-dimensional subspace may be canonically extended to extreme functions on the whole space.

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