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A Weak* Similarity Degree Characterization for Injective von Neumann Algebras

A Weak* Similarity Degree Characterization for Injective von Neumann Algebras
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摘要 In this note, we show that avon Neumann algebra M is injective if and only if the weak＊ similarity degree d.（M） ≤ 2. In this note, we show that avon Neumann algebra M is injective if and only if the weak＊ similarity degree d.（M） ≤ 2.
作者 Zhe DONG Ya Fei ZHAO
机构地区 Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第10期1689-1697,共9页 数学学报（英文版）
基金 Supported by the Zhejiang Qianjiang Talent Program in 2008 the Program for New Century Excellent Talents in University of Ministry of Education of China in 2010 the National Natural Science Foundation of China(Grant No.11271321) the Fundamental Research Funds of Zhejiang University
关键词 Weak＊ similarity degree injective von Neumann algebra operator space Weak＊ similarity degree, injective von Neumann algebra, operator space
分类号 O177.5 [理学—基础数学] TP18 [自动化与计算机技术—控制理论与控制工程]
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参考文献16

  • 1Brown, N.P. , Ozawa, N. : C*-Algebras and Finite Dimensional Approximations, American Mathematical Society, Rhode Island, 2008.
  • 2Christensen, E. : On non self-adjoint representations of operator algebras.Amer.J.Math. , 103, 817–834 (1981).
  • 3Connes, A. : Classification of injective factors, Cases II1, II∞, IIIλ, λ ≠ 1.Ann.of Math. , 104, 73–115 (1976).
  • 4Effros, E.G. , Ruan, Z.J. : Operator Spaces, Oxford University Press, New York, 2000.
  • 5Effros, E.G. , Ruan, Z.J. : Operator space tensor products and Hopf convolution algebras.J.Operator Theory, 50, 131–156 (2003).
  • 6Elliott, G. : On approximately finite-dimensional von Neumann algebras.Math.Scand. , 39, 91–101 (1976).
  • 7Elliott, G. : On approximately finite-dimensional von Neumann algebras, II.Canadian.Bull. , 21, 415–418 (1978).
  • 8Haagerup, U. : Solution of the similarity problem for cyclic representations of C*-algebras.Ann.of Math. , 118(2), 215–240 (1983).
  • 9Kadison, R. : On the orthogonalization of operator representations.Amer.J.Math. , 77, 600–620 (1955).
  • 10Le Merdy, C. : The weak* similarity property on dual operator algebras.Integr.Equ.Oper.Theory, 37, 72–94 (2000).
Acta Mathematica Sinica,English Series
2014年 第10期

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