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
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
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چکیده انگلیسی
Amenability for groups can be extended to metric spaces, algebras over commutative fields and Câ-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 Cuâ(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 Cuâ(X) is algebraically amenable (3) Cuâ(X) has a tracial state; (4) Cuâ(X) is not properly infinite; (5) [1]0â [0]0 in the K0-group K0(Cuâ(X)); (6) Cuâ(X) does not contain the Leavitt algebra as a unital â-subalgebra; (7) Cuâ(X) is a Følner Câ-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 Cuâ(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
Journal: Journal of Mathematical Analysis and Applications - Volume 459, Issue 2, 15 March 2018, Pages 686-716
نویسندگان
Pere Ara, Kang Li, Fernando Lledó, Jianchao Wu,