Extreme points of unit balls in Lipschitz function spaces

Smarzewski, Ryszard

doi:10.1090/S0002-9939-97-03866-5

Extreme points of unit balls in Lipschitz function spaces
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Proc. Amer. Math. Soc. 125 (1997), 1391-1397 Request permission

Abstract:

We give a new characterization of the set $\operatorname {ext}\left ( B_{X^{\#}}\right )$ of all extreme points of the unit ball $B_{X^{\#}}$ in the Banach space $X^{\#}$ of all Lipschitz functions on a metric space $X.$ This result is applied to get a total variation characterization of $\operatorname {ext}\left ( B_{X^{\#}}\right )$ in the particular case when $X$ is a convex subset of a Banach space.

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