تقرير
On the structure of the Cuntz semigroup in (possibly) nonunital C*-algebras
| العنوان: | On the structure of the Cuntz semigroup in (possibly) nonunital C*-algebras |
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| المؤلفون: | Tikuisis, Aaron, Toms, Andrew |
| المصدر: | Canadian Mathematical Bulletin, Volume 58, Number 2 (2015), pp. 402-414 |
| سنة النشر: | 2012 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Operator Algebras, Mathematics - Functional Analysis, 46L35, 46L80, 46L05, 47L40, 46L85 |
| الوصف: | We examine the ranks of operators in semi-finite C*-algebras as measured by their densely defined lower semicontinuous traces. We first prove that a unital simple C*-algebra whose extreme tracial boundary is nonempty and finite contains positive operators of every possible rank, independent of the property of strict comparison. We then turn to nonunital simple algebras and establish criteria that imply that the Cuntz semigroup is recovered functorially from the Murray-von Neumann semigroup and the space of densely defined lower semicontinuous traces. Finally, we prove that these criteria are satisfied by not-necessarily-unital approximately subhomogeneous algebras of slow dimension growth. Comment: 13 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.4153/CMB-2014-040-5 |
| URL الوصول: | http://arxiv.org/abs/1210.2235 |
| رقم الأكسشن: | edsarx.1210.2235 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.4153/CMB-2014-040-5 |
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