On the extension of isometries between the unit spheres of von Neumann algebras

被引：29

作者：

Fernandez-Polo, Francisco J. ^{[1
]}

Peralta, Antonio M. ^{[1
]}

机构：

[1] Univ Granada, Fac Ciencias, Dept Anal Matemat, E-18071 Granada, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 466卷 / 01期

关键词：

Tingley's problem; Extension of isometrics; von Neumann algebra; JB-ASTERISK-TRIPLES; C-STAR-ALGEBRAS; TINGLEYS PROBLEM; BANACH-SPACES; REPRESENTATION THEOREM; FACIAL STRUCTURE; OPERATORS; MAPPINGS; ELEMENTS;

D O I：

10.1016/j.jmaa.2018.05.062

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that every surjective isometry between the unit spheres of two von Neumann algebras admits a unique extension to a surjective real linear isometry between these two algebras. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：127 / 143

页数：17

共 50 条

[1] On extension of isometries and approximate isometries between unit spheres
Liu, Rui
Zhang, Lun
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 352 (02) : 749 - 761
[2] Isometries between projection lattices of von Neumann algebras
Mori, Michiya
JOURNAL OF FUNCTIONAL ANALYSIS, 2019, 276 (11) : 3511 - 3528
[3] On extension of isometries between unit spheres of L∞ and E
Li, Lei
Ren, Weiyun
QUAESTIONES MATHEMATICAE, 2008, 31 (03) : 209 - 218
[4] On the Extension of Isometries between Unit Spheres of E and C(Ω)
Guang Gui Ding
Acta Mathematica Sinica, 2003, 19 : 793 - 800
[5] On the extension of isometries between unit spheres of E and C(Ω)
Ding, GG
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2003, 19 (04) : 793 - 800
[6] On extension of isometries between the positive unit spheres of (Σ lp)lq
Sun, Longfa
Sun, Yinghua
Li, Lei
Zheng, Zheming
POSITIVITY, 2024, 28 (05)
[7] ON THE EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF A -TRIPLE AND A BANACH SPACE
Becerra-Guerrero, Julio
Cueto-Avellaneda, Maria
Fernandez-Polo, Francisco J.
Peralta, Antonio M.
JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2021, 20 (01) : 277 - 303
[8] Extension of isometries between the unit spheres of p-normed spaces
Jian-Zhong Xiao
Ying Lu
Annals of Functional Analysis, 2022, 13
[9] Extension of Isometries Between the Unit Spheres of Normed Space E and C (Ω)
Xi Nian Fang
Jian Hua Wang
Acta Mathematica Sinica, 2006, 22 : 1819 - 1824
[10] Extension of Isometries Between the Unit Spheres of Normed Space E and C(Ω)
Xi Nian FANG Department of Applied Mathematics
ActaMathematicaSinica(EnglishSeries), 2006, 22 (06) : 1819 - 1824

← 1 2 3 4 5 →