Amenable and inner amenable actions and approximation properties for crossed products by locally compact groups
نویسندگان
چکیده
Abstract Amenable actions of locally compact groups on von Neumann algebras are investigated by exploiting the natural module structure crossed product over Fourier algebra acting group. The resulting characterization injectivity for products generalizes a result Anantharaman-Delaroche discrete groups. $C^*$ -algebras in same way, and amenability action is related to nuclearity corresponding product. A survey given show that this notion amenable satisfies number expected properties. inner introduced, applications form averaging arguments, relating approximation properties components underlying $w^*$ -dynamical system. We use these results answer recent question Buss, Echterhoff, Willett.
منابع مشابه
Amenable Actions and Exactness for Discrete Groups
It is proved that a discrete group G is exact if and only if its left translation action on the Stone-Čech compactification is amenable. Combining this with an unpublished result of Gromov, we have the existence of non exact discrete groups. In [KW], Kirchberg and Wassermann discussed exactness for groups. A discrete group G is said to be exact if its reduced group C-algebra C λ(G) is exact. Th...
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Since 1929 when von Neumann [vN29] introduced the notion of an invariant mean on a group (and more generally on a G-set) there is a permanent interest in the study of the phenomenon known as amenability. Amenable objects like groups, semigroups, algebras, graphs, metric spaces, operator algebras etc. play an important role in different areas of mathematics. A big progress in understanding of th...
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ژورنال
عنوان ژورنال: Canadian mathematical bulletin
سال: 2021
ISSN: ['1496-4287', '0008-4395']
DOI: https://doi.org/10.4153/s0008439521000333