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.

引用

页码：195 / 201

页数：7

共 45 条

[21] On measure concentration for separately Lipschitz functions in product spaces
Vidmantas Bentkus
Israel Journal of Mathematics, 2007, 158 : 1 - 17
[22] Isometric representations of weighted spaces of little Lipschitz functions
A. Jiménez-Vargas
P. Rueda
Revista Matemática Complutense, 2018, 31 : 333 - 350
[23] Weakly compact composition operators on spaces of Lipschitz functions
Jimenez-Vargas, A.
POSITIVITY, 2015, 19 (04) : 807 - 815
[24] Weakly compact composition operators on spaces of Lipschitz functions
A. Jiménez-Vargas
Positivity, 2015, 19 : 807 - 815
[25] 2-Local Isometries on Spaces of Lipschitz Functions
Jimenez-Vargas, A.
Villegas-Vallecillos, Moises
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2011, 54 (04): : 680 - 692
[26] QUASICONTINUITY OF NEWTON-SOBOLEV FUNCTIONS AND DENSITY OF LIPSCHITZ FUNCTIONS ON METRIC SPACES
Bjoern, Anders
Bjoern, Jana
Shanmugalingam, Nageswari
HOUSTON JOURNAL OF MATHEMATICS, 2008, 34 (04): : 1197 - 1211
[27] Boundedness of Commutators with Lipschitz Functions in Non-homogeneous Spaces*
Xiaoli Fu
Yan Meng
Dachun Yang
Chinese Annals of Mathematics, Series B, 2007, 28 : 67 - 80
[28] ON INTERMEDIATE DIFFERENTIABILITY OF LIPSCHITZ FUNCTIONS ON CERTAIN BANACH-SPACES
FABIAN, M
PREISS, D
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 113 (03) : 733 - 740
[29] A note on the algebraic reflexivity of the group of surjective isometries of K-(C(K))
Rao, T. S. S. R. K.
EXPOSITIONES MATHEMATICAE, 2008, 26 (01) : 79 - 83
[30] Boundedness of Commutators with Lipschitz Functions in Non-homogeneous Spaces
Xiaoli FU Yan MENG Dachun YANG School of Mathematical Sciences
School of Information
Chinese Annals of Mathematics, 2007, (01) : 67 - 80

← 1 2 3 4 5 →