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

[11] Extension of isometries between the unit spheres of p-normed spaces
Xiao, Jian-Zhong
Lu, Ying
ANNALS OF FUNCTIONAL ANALYSIS, 2022, 13 (02)
[12] On extension of isometries between the positive unit spheres of c0(Γ)
Sun, Longfa
Zhang, Yipeng
Sun, Yinghua
Dai, Duanxu
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2024,
[13] Extension of isometries between the unit spheres of normed space E and C (Ω)
Fang, Xi Nian
Wang, Jian Hua
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2006, 22 (06) : 1819 - 1824
[14] Rearrangements of Tripotents and Differences of Isometries in Semifinite von Neumann Algebras
Bikchentaev, A. M.
LOBACHEVSKII JOURNAL OF MATHEMATICS, 2019, 40 (10) : 1450 - 1454
[15] Rearrangements of Tripotents and Differences of Isometries in Semifinite von Neumann Algebras
A. M. Bikchentaev
Lobachevskii Journal of Mathematics, 2019, 40 : 1450 - 1454
[16] EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF COMPLEX lp(Γ)(p > 1) SPACES
伊继金
王瑞东
王晓晓
Acta Mathematica Scientia, 2014, 34 (05) : 1540 - 1550
[17] EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF COMPLEX lp(Γ)(p > 1) SPACES
Yi, Jijin
Wang, Ruidong
Wang, Xiaoxiao
ACTA MATHEMATICA SCIENTIA, 2014, 34 (05) : 1540 - 1550
[18] ISOMETRIES OF LP-SPACES ASSOCIATED WITH FINITE VON NEUMANN ALGEBRAS
RUSSO, B
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1968, 74 (02) : 228 - &
[19] ISOMETRIES OF BANACH-ALGEBRAS SATISFYING THE VON-NEUMANN-INEQUALITY
ARAZY, J
MATHEMATICA SCANDINAVICA, 1994, 74 (01) : 137 - 151
[20] On extension of isometries between unit spheres of L∞ (Γ)-type space and a Banach space E
Liu, Rui
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 333 (02) : 959 - 970

← 1 2 3 4 5 →