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The Cuntz Comparison in the Standard -Algebra

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  • Xiaochun Fang
  • Nung-Sing Sze
  • Xiao-Ming Xu

Abstract

The Cuntz comparison, introduced by Cuntz in early 1978, associates each -algebra with an abelian semigroup which is an invariant for the classification of the nuclear -algebras and called the Cuntz semigroup. In this paper, we study the Cuntz comparison in the standard -algebra. We characterize the Cuntz comparison in terms of the dimension of the operator range. Also, we consider the structure of the semilinear map which preserves the Cuntz comparison.

Suggested Citation

  • Xiaochun Fang & Nung-Sing Sze & Xiao-Ming Xu, 2014. "The Cuntz Comparison in the Standard -Algebra," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-4, June.
    • Handle: RePEc:hin:jnlaaa:623520
    DOI: 10.1155/2014/623520
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