Abstract and Applied Analysis (Jan 2014)

The Cuntz Comparison in the Standard C*-Algebra

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

DOI
https://doi.org/10.1155/2014/623520
Journal volume & issue
Vol. 2014

Abstract

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The Cuntz comparison, introduced by Cuntz in early 1978, associates each C*-algebra with an abelian semigroup which is an invariant for the classification of the nuclear C*-algebras and called the Cuntz semigroup. In this paper, we study the Cuntz comparison in the standard C*-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.