The Cuntz Comparison in the Standard C*-Algebra
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 characteri...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/623520 |
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| _version_ | 1832557051653390336 |
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| author | Xiaochun Fang Nung-Sing Sze Xiao-Ming Xu |
| author_facet | Xiaochun Fang Nung-Sing Sze Xiao-Ming Xu |
| author_sort | Xiaochun Fang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-bfd9c415c41f4172b7632b8597cf2fb1 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-bfd9c415c41f4172b7632b8597cf2fb12025-02-03T05:43:49ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/623520623520The Cuntz Comparison in the Standard C*-AlgebraXiaochun Fang0Nung-Sing Sze1Xiao-Ming Xu2Department of Mathematics, Tongji University, Shanghai 200092, ChinaDepartment of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong KongSchool of Science, Shanghai Institute of Technology, Shanghai 201418, ChinaThe 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.http://dx.doi.org/10.1155/2014/623520 |
| spellingShingle | Xiaochun Fang Nung-Sing Sze Xiao-Ming Xu The Cuntz Comparison in the Standard C*-Algebra Abstract and Applied Analysis |
| title | The Cuntz Comparison in the Standard C*-Algebra |
| title_full | The Cuntz Comparison in the Standard C*-Algebra |
| title_fullStr | The Cuntz Comparison in the Standard C*-Algebra |
| title_full_unstemmed | The Cuntz Comparison in the Standard C*-Algebra |
| title_short | The Cuntz Comparison in the Standard C*-Algebra |
| title_sort | cuntz comparison in the standard c algebra |
| url | http://dx.doi.org/10.1155/2014/623520 |
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