Biseparating maps between Lipschitz function spaces

被引：25

作者：

Araujo, Jesus ^{[1
]}

Dubarbie, Luis ^{[1
]}

机构：

[1] Univ Cantabria, Dept MATESCO, Fac Ciencias, E-39071 Santander, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 357卷 / 01期

关键词：

Biseparating map; Disjointness preserving map; Automatic continuity; Lipschitz function; BANACH-STONE THEOREMS; AUTOMATIC-CONTINUITY; SEPARATING MAPS; DIFFERENTIABLE FUNCTIONS; LINEAR ISOMETRIES; ALGEBRAS; OPERATORS; REALCOMPACTNESS;

D O I：

10.1016/j.jmaa.2009.03.065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For complete metric spaces X and Y, a description of linear biseparating maps between spaces of vector-valued Lipschitz functions defined on X and Y is provided. In particular it is proved that X and Y are bi-Lipschitz homeomorphic, and the automatic continuity of such maps is derived in some cases. Besides, these results are used to characterize the separating bijections between scalar-valued Lipschitz function spaces when Y is compact. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：191 / 200

页数：10

共 26 条

[1] Abramovich YA, 2000, MEM AM MATH SOC, V143, pVIII
[2] Realcompactness and Banach-stone theorems
Araujo, J
[J]. BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2004, 11 (02) : 247 - 258
[3] Linear biseparating maps between spaces of vector-valued differentiable functions and automatic continuity
Araujo, J
[J]. ADVANCES IN MATHEMATICS, 2004, 187 (02) : 488 - 520
[4] Automatic continuity of biseparating maps
Araujo, J
Jarosz, K
[J]. STUDIA MATHEMATICA, 2003, 155 (03) : 231 - 239
[5] Separating maps and linear isometries between some spaces of continuous functions
Araujo, J
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 226 (01) : 23 - 39
[6] Realcompactness and spaces of vector-valued functions
Araujo, J
[J]. FUNDAMENTA MATHEMATICAE, 2002, 172 (01) : 27 - 40
[7] Linear isometries on subalgebras of uniformly continuous functions
Araujo, J
Font, JJ
[J]. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2000, 43 : 139 - 147
[8] BUSTAMANTE J, 2000, MONATSH MATH, V129, P25
[9] DUBARBIE L, CANAD MATH IN PRESS
[10] ON SEPARATING MAPS BETWEEN LOCALLY COMPACT SPACES
FONT, JJ
HERNANDEZ, S
[J]. ARCHIV DER MATHEMATIK, 1994, 63 (02) : 158 - 165

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