Let (X, d X) and (Y,d Y) be pointed compact metric spaces with distinguished base points e X and e Y. The Banach algebra of all -valued Lipschitz functions on X - where is either‒or ℝ - that map the base point e X to 0 is denoted by Lip0(X). The peripheral range of a function f ∈ Lip0(X) is the set Ranµ(f) = f(x): |f(x)| = ‖f‖∞ of range values of maximum modulus. We prove that if T 1, T 2: Lip0(X) → Lip0(Y) and S 1, S 2: Lip0(X) → Lip0(X) are surjective mappings such that for all f, g ∈ Lip0(X), then there are mappings φ1φ2: Y → with φ1(y)φ2(y) = 1 for all y ∈ Y and a base point-preserving Lipschitz homeomorphism ψ: Y → X such that T j(f)(y) = φ j(y)S j(f)(ψ(y)) for all f ∈ Lip0(X), y ∈ Y, and j = 1, 2. In particular, if S 1 and S 2 are identity functions, then T 1 and T 2 are weighted composition operators.
@article{bwmeta1.element.doi-10_2478_s11533-013-0243-7,
author = {Antonio Jim\'enez-Vargas and Kristopher Lee and Aaron Luttman and Mois\'es Villegas-Vallecillos},
title = {Generalized weak peripheral multiplicativity in algebras of Lipschitz functions},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {1197-1211},
zbl = {1298.46043},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0243-7}
}
Antonio Jiménez-Vargas; Kristopher Lee; Aaron Luttman; Moisés Villegas-Vallecillos. Generalized weak peripheral multiplicativity in algebras of Lipschitz functions. Open Mathematics, Tome 11 (2013) pp. 1197-1211. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0243-7/
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