کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4592043 | 1335070 | 2010 | 21 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Ranks of operators in simple C∗-algebras
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let A be a unital simple separable C∗-algebra with strict comparison of positive elements. We prove that the Cuntz semigroup of A is recovered functorially from the Murray–von Neumann semigroup and the tracial state space T(A) whenever the extreme boundary of T(A) is compact and of finite covering dimension. Combined with a result of Winter, we obtain Z⊗A≅A whenever A moreover has locally finite decomposition rank. As a corollary, we confirm Elliott's classification conjecture under reasonably general hypotheses which, notably, do not require any inductive limit structure. These results all stem from our investigation of a basic question: what are the possible ranks of operators in a unital simple C∗-algebra?
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 259, Issue 5, 1 September 2010, Pages 1209-1229
Journal: Journal of Functional Analysis - Volume 259, Issue 5, 1 September 2010, Pages 1209-1229