Some results on isometric composition operators on Lipschitz spaces

2019/10/17 by Abraham Rueda Zoca, Zoca, Abraham Rueda
Mathematics · #46B20 #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary 47B33 #Secondary 47B38

paper · pdf · doi:10.48550/arxiv.1910.07923

openalex publication_date 2019/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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_ϕ:Lip₀(M)\longrightarrow Lip₀(N) is isometric depending on the properties of ϕ. We obtain a complete characterisation of those operators C_ϕ in terms of a property of the function ϕ in the case that B_{\mathcal F(M)} is the closed convex hull of its preserved extreme points. Also, we obtain necessary and sufficient conditions for C_ϕ being isometric in the case that M is geodesic.

Citations

• The Daugavet property for spaces of Lipschitz functions
• A characterisation of the Daugavet property in spaces of Lipschitz\n functions

Related

• Isometric composition operators on Lipschitz spaces
• Noncompactness and noncompleteness in isometries of Lipschitz spaces
• On isometric embeddings into the set of strongly norm-attaining Lipschitz functions
• 2-local standard isometries on vector-valued Lipschitz function spaces
• Weighted composition operators preserving various Lipschitz constants