Some results on isometric composition operators on Lipschitz spaces

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Publication date: 17 October 2019

Abstract: Given two metric spaces

M

and

N

we study, motivated by a question of N. Weaver, conditions under which an isometric composition operator

C_{p} h i : m a t h r m {L i p}_{0} (M) l o n g r i g h t a r r o w m a t h r m {L i p}_{0} (N)

is isometric depending on the properties of

p h i

. We obtain a complete characterisation of those operators

C_{p} h i

in terms of a property of the function

p h i

in the case that

B_{m a t h c a l F (M)}

is the closed convex hull of its preserved extreme points. Also, we obtain necessary and sufficient conditions for

C_{p} h i

being isometric in the case that

M

is geodesic.

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