Some results on isometric composition operators on Lipschitz spaces
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AbstractGiven two metric spaces M and N we study, motivated by a question of N. Weaver, conditions under which a composition operator $$C_\phi :{\mathrm {Lip}}_0(M)\longrightarrow {\mathrm {Lip}}_0(N)$$ C ϕ : Lip 0 ( M ) ⟶ Lip 0 ( N ) is an isometry depending on the properties of $$\phi $$ ϕ . We obtain a complete characterisation of those operators $$C_\phi $$ C ϕ in terms of a property of the function $$\phi $$ ϕ in the case that $$B_{{\mathcal {F}}(M)}$$ B F ( M ) is the closed convex hull of its preserved extreme points. Also, we obtain necessary condition for $$C_\phi $$ C ϕ being an isometry in the case that M is geodesic.
2008 ◽
Vol 347
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pp. 72-80
1964 ◽
Vol 15
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pp. 256-256
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1996 ◽
Vol 60
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pp. 245-254
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1976 ◽
Vol 80
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pp. 269-276
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2012 ◽
Vol 2012
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pp. 1-8
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1994 ◽
Vol 116
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pp. 500-507
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2012 ◽
Vol 220-223
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pp. 2466-2470
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2010 ◽
Vol 81
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pp. 465-472
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