Algebraic reflexivity of the isometry group of some spaces of Lipschitz functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:366

Article

Jimenez-Vargas, A.¹  Morales Campoy, A.¹  Villegas-Vallecillos, Moises¹ 

[1] Univ Almeria, Dept Algebra & Anal Matemat, Almeria 04120, Spain

关键词: Iso-reflexive space;    Algebraic reflexivity;    Isometry group;    Lipschitz function;    Isometric reflection;    Generalized bi-circular projection;   

DOI  :  10.1016/j.jmaa.2010.01.034

来源: Elsevier

【 摘 要 】

We show that the isometry groups of Lip(X, d) and lip(X, d(alpha)) with alpha is an element of (0, 1), for a compact metric space (X. d), are algebraically reflexive. We also prove that the sets of isometric reflections and generalized bi-circular projections on such spaces are algebraically reflexive. In order to achieve this, we characterize generalized bi-circular projections on these spaces. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free