کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8900126 1631557 2018 31 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Amenability and uniform Roe algebras
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Amenability and uniform Roe algebras
چکیده انگلیسی
Amenability for groups can be extended to metric spaces, algebras over commutative fields and C⁎-algebras by adapting the notion of Følner nets. In the present article we investigate the close ties among these extensions and show that these three pictures unify in the context of the uniform Roe algebra Cu⁎(X) over a metric space (X,d) with bounded geometry. In particular, we show that the following conditions are equivalent: (1) (X,d) is amenable; (2) the translation algebra generating Cu⁎(X) is algebraically amenable (3) Cu⁎(X) has a tracial state; (4) Cu⁎(X) is not properly infinite; (5) [1]0≠[0]0 in the K0-group K0(Cu⁎(X)); (6) Cu⁎(X) does not contain the Leavitt algebra as a unital ⁎-subalgebra; (7) Cu⁎(X) is a Følner C⁎-algebra in the sense that it admits a net of unital completely positive maps into matrices which is asymptotically multiplicative in the normalized trace norm. We also show that every possible tracial state of the uniform Roe algebra Cu⁎(X) is amenable.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 459, Issue 2, 15 March 2018, Pages 686-716
نویسندگان
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