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
相关论文
共 50 条
  • [31] The range of operators on von Neumann algebras
    Bermúdez, T
    Kalton, NJ
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (05) : 1447 - 1455
  • [32] MAHARAM TRACES ON VON NEUMANN ALGEBRAS
    Chilin, V. I.
    Zakirov, B. S.
    METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, 2010, 16 (02): : 101 - 111
  • [33] LIFTING INVERTIBLES IN VON NEUMANN ALGEBRAS
    ROGERS, RR
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 113 (02) : 381 - 388
  • [34] Hypercontractivity in group von Neumann algebras
    JUNGE, M. A. R. I. U. S.
    PALAZUELOS, C. A. R. L. O. S.
    PARCET, J. A. V. I. E. R.
    PERRIN, M. A. T. H. I. L. D. E.
    MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 249 (1183) : VII - +
  • [35] Infinite Measures on von Neumann Algebras
    Stanisław Goldstein
    Adam Paszkiewicz
    International Journal of Theoretical Physics, 2015, 54 : 4341 - 4348
  • [36] Commutator estimates in von Neumann algebras
    Ber, A. F.
    Sukochev, F. A.
    FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2013, 47 (01) : 62 - 63
  • [37] Rohlin Flows on von Neumann Algebras
    Masuda, Toshihiko
    Tomatsu, Reiji
    MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 244 (1153) : VII - +
  • [38] HNN extensions of von Neumann algebras
    Ueda, Y
    JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 225 (02) : 383 - 426
  • [39] Stochastic coupling for von Neumann algebras
    Cecchini, C
    MATHEMATICAL NOTES, 1999, 65 (5-6) : 638 - 648
  • [40] The Mazur-Ulam property for commutative von Neumann algebras
    Cueto-Avellaneda, Maria
    Peralta, Antonio M.
    LINEAR & MULTILINEAR ALGEBRA, 2020, 68 (02) : 337 - 362
12345