Isometries between projection lattices of von Neumann algebras

被引：15
|
作者：
Mori, Michiya [1 ]
机构：
[1] Univ Tokyo, Grad Sch Math Sci, Tokyo 1538914, Japan
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2019年 / 276卷 / 11期
关键词：
von Neumann algebra; Projection; Isometry; Grassmann space; WIGNER-TYPE THEOREM; TINGLEYS PROBLEM; TRANSFORMATIONS; SPACES;
D O I：
10.1016/j.jfa.2018.10.011
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate surjective isometries between projection lattices of two von Neumann algebras. We show that such a mapping is characterized by means of Jordan *-isomorphisms. In particular, we prove that two von Neumann algebras without type I-1 direct summands are Jordan *-isomorphic if and only if their projection lattices are isometric. Our theorem extends the recent result for type I factors by G.P. Geher and P. Semrl, which is a generalization of Wigner's theorem. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码：3511 / 3528
页数：18
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