Abstract and Applied Analysis

The Cuntz Comparison in the Standard ${\mathbf{C}}^{\mathbf{\ast}}$-Algebra

Abstract

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

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 623520, 4 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412277038

Digital Object Identifier
doi:10.1155/2014/623520

Mathematical Reviews number (MathSciNet)
MR3219378

Citation

Fang, Xiaochun; Sze, Nung-Sing; Xu, Xiao-Ming. The Cuntz Comparison in the Standard ${\mathbf{C}}^{\mathbf{\ast}}$ -Algebra. Abstr. Appl. Anal. 2014 (2014), Article ID 623520, 4 pages. doi:10.1155/2014/623520. https://projecteuclid.org/euclid.aaa/1412277038

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