The Cuntz Comparison in the Standard -Algebra

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.

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