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

被引：12
|
作者：
Jimenez-Vargas, A. [1 ]
Morales Campoy, A. [1 ]
Villegas-Vallecillos, Moises [1 ]
机构：
[1] Univ Almeria, Dept Algebra & Anal Matemat, Almeria 04120, Spain
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 366卷 / 01期
关键词：
Iso-reflexive space; Algebraic reflexivity; Isometry group; Lipschitz function; Isometric reflection; Generalized bi-circular projection; BI-CIRCULAR PROJECTIONS; LOCAL ISOMETRIES; BANACH ALGEBRAS; MAXIMAL IDEALS;
D O I：
10.1016/j.jmaa.2010.01.034
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
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页码：195 / 201
页数：7
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