2020/12/28 by Andrew McKee, McKee, Andrew, Reyhaneh Pourshahami +1 · 1 citation
Materials Science · Mathematics · Medicine · #46L55 #Advanced Operator Algebra Research #FOS: Mathematics #Neurological disorders and treatments #Operator Algebras (math.OA) #Organic and Molecular Conductors Research
paper · pdf · doi:10.48550/arxiv.2012.14455
openalex publication_date 2020/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Amenable actions of locally compact groups on von Neumann algebras are\ninvestigated by exploiting the natural module structure of the crossed product\nover the Fourier algebra of the acting group. The resulting characterisation of\ninjectivity for crossed products generalises a result of Anantharaman-Delaroche\non discrete groups. Amenable actions of locally compact groups on\nC^*-algebras are investigated in the same way, and amenability of the action\nis related to nuclearity of the corresponding crossed product. A survey is\ngiven to show that this notion of amenable action for C^*-algebras satisfies\na number of expected properties. A notion of inner amenability for actions of\nlocally compact groups is introduced, and a number of applications are given in\nthe form of averaging arguments, relating approximation properties of crossed\nproduct von Neumann algebras to properties of the components of the underlying\nw^*-dynamical system. We use these results to answer a recent question of\nBuss-Echterhoff-Willett.\n