Perturbations of certain crossed product algebras by free groups

被引:1
作者
Chan, Wai-Kit [1 ]
机构
[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
基金
美国国家科学基金会;
关键词
Von Neumann algebras; Perturbation; Crossed product algebras; INCLUSIONS; II1;
D O I
10.1016/j.jfa.2014.09.014
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Given two von Neumann algebras M and N acting on the same Hilbert space, d(M, N) is defined to be the Hausdorff distance between their unit balls. The Kadison-Kastler problem asks whether two sufficiently close von Neumann algebras are spatially isomorphic. In this article, we show that if P-0 is an injective von Neumann algebra with a cyclic tracial vector, G is a free group, a is a free action of G on P-0 and N is a von Neumann algebra such that d(N, P-0 (sic)(alpha) G) < 1/7 X 10(-7), then N and P-0 unknown symble alpha G are spatially isomorphic. Suitable choices of the actions give the first examples of infinite noninjective factors for which this problem has a positive solution. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码:3994 / 4027
页数:34
相关论文
共 29 条
  • [11] Perturbations of nuclear C*-algebras
    Christensen, Erik
    Sinclair, Allan M.
    Smith, Roger R.
    White, Stuart A.
    Winter, Wilhelm
    [J]. ACTA MATHEMATICA, 2012, 208 (01) : 93 - 150
  • [12] PERTURBATIONS OF C*-ALGEBRAIC INVARIANTS
    Christensen, Erik
    Sinclair, Allan
    Smith, Roger R.
    White, Stuart
    [J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2010, 20 (02) : 368 - 397
  • [13] CLASSIFICATION OF INJECTIVE FACTORS - CASES II1, II INFINITY, III LAMBDA, LAMBDA NOT-EQUAL-TO 1
    CONNES, A
    [J]. ANNALS OF MATHEMATICS, 1976, 104 (01) : 73 - 115
  • [14] STANDARD AND SPLIT INCLUSIONS OF VONNEUMANN-ALGEBRAS
    DOPLICHER, S
    LONGO, R
    [J]. INVENTIONES MATHEMATICAE, 1984, 75 (03) : 493 - 536
  • [15] ELLIOTT GA, 1978, CANAD MATH B, V21, P415
  • [16] Groupoid normalizers of tensor products
    Fang, Junsheng
    Smith, Roger R.
    White, Stuart A.
    Wiggins, Alan D.
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 258 (01) : 20 - 49
  • [18] HOUDAYER C, ARXIV12031254
  • [19] JOHNSON BE, 1977, P LOND MATH SOC, V34, P439
  • [20] PERTURBATIONS OF VONNEUMANN NEUMANN ALGEBRAS I STABILITY OF TYPE
    KADISON, RV
    KASTLER, D
    [J]. AMERICAN JOURNAL OF MATHEMATICS, 1972, 94 (01) : 38 - &