Abstract
Let be a compact Hausdorff space, be a continuous involution on and denote the uniformly closed real subalgebra of consisting of all for which . Let be a compact metric space and let denote the complex Banach space of complex-valued Lipschitz functions of order on under the norm , where . For , the closed subalgebra of consisting of all for which as , denotes by . Let be a Lipschitz involution on and define for and for . In this paper, we give a characterization of extreme points of , where is a real linear subspace of or which contains 1, in particular, or .
Highlights
Introduction and PreliminariesWe let R, C, and T {z ∈ C : |z| 1} denote the field of real numbers, complex numbers, and the unit circle, respectively
We denote by X∗ and BX the dual space X and the closed unit ball of X, respectively
The set of all HahnBanach extensions of φ to X will be denoted by Hφ
Summary
Let X be a compact Hausdorff space, τ be a continuous involution on X and C X, τ denote the uniformly closed real subalgebra of C X consisting of all f ∈ C X for which f ◦ τ f. Let τ be a Lipschitz involution on X, d and define Lip X, τ, dα Lip X, dα ∩ C X, τ for α ∈ 0, 1 and lip X, τ, dα lip X, dα ∩ C X, τ for α ∈ 0, 1.
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