• Title/Summary/Keyword: type $II_infty$ factor

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Essentially normal elements of von neumann algebras

  • Cho, Sung-Je
    • Communications of the Korean Mathematical Society
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    • v.10 no.3
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    • pp.653-659
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    • 1995
  • We prove that two essentially normal elements of a type $II_{\infty}$ factor von Neumann algebra are unitarily equivalent up to the compact ideal if and only if they have the identical essential spectrum and the same index data. Also we calculate the spectrum and essential spectrum of a non-unitary isometry of von Neumann algebra.

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On Factor States on a Fixed Point Algebra of a UHF Algebra by the Torus Action II

  • Byun, Chang-Ho
    • Honam Mathematical Journal
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    • v.7 no.1
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    • pp.119-127
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    • 1985
  • A study is made of a special type of $C^{\ast}$ -dynamical systems, consisting of a class $n^{\infty}$ uniformly hyperfinite $C^{\ast}$-algebra A, the torus group $G=T^{d}$ ($$1{\leq_-}d{\leq_-}n-1$$) and a natural product action of G on A by $^{*}-automorphisms$. We give some conditions for product states on the fixed point algebra $A^{G}$ of A by G to be factorial.

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