Moisés Villegas-Vallecillos

LINEAR ISOMETRIES BETWEEN SPACES OF VECTOR-VALUED LIPSCHITZ FUNCTIONS

In this paper we state a Lipschitz version of a theorem due to Cambern concerning into linear isometries between spaces of vector-valued continuous functions and deduce a Lipschitz version of a celebrated theorem due to Jerison concerning onto linear isometries between such spaces.

Generalized weak peripheral multiplicativity in algebras of Lipschitz functions

Let (X, dX) and (Y,dY) be pointed compact metric spaces with distinguished base points eX and eY. The Banach algebra of all

2 -Local Isometries on Spaces of Lipschitz Functions

\mathbb{K}

Hermitian operators on Banach algebras of Lipschitz functions

-valued Lipschitz functions on X — where

The uniform separation property and Banach-Stone theorems for lattice-valued Lipschitz functions

\mathbb{K}

Essential Norm of Composition Operators on Banach Spaces of Hölder Functions

is either‒or ℝ — that map the base point eX 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 T1, T2: Lip0(X) → Lip0(Y) and S1, S2: Lip0(X) → Lip0(X) are surjective mappings such that

Duality for ideals of Lipschitz maps

Ran_\pi (T_1 (f)T_2 (g)) \cap Ran_\pi (S_1 (f)S_2 (g)) \ne \emptyset

Weakly peripherally multiplicative surjections of pointed Lipschitz algebras

for all f, g ∈ Lip0(X), then there are mappings φ1φ2: Y →

Into linear isometries between spaces of Lipschitz functions

\mathbb{K}

Lipschitz compact operators

with φ1(y)φ2(y) = 1 for all y ∈ Y and a base point-preserving Lipschitz homeomorphism ψ: Y → X such that Tj(f)(y) = φj(y)Sj(f)(ψ(y)) for all f ∈ Lip0(X), y ∈ Y, and j = 1, 2. In particular, if S1 and S2 are identity functions, then T1 and T2 are weighted composition operators.