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• W1517553774 abstract "In this paper, we study bimodules over a von Neumann algebra $M$ in two related contexts. The first is an inclusion $M subseteq M rtimes_alpha G$, where $G$ is a discrete group acting on a factor $M$ by outer automorphisms. The second is a regular inclusion $M subseteq N$ of finite factors. In the case of crossed products, we characterize the $M$-bimodules $X$ that lie between $M$ and $M rtimes_alpha G$ and are closed in the Bures topology, in terms of the subsets of $G$. We show that this characterization also holds for $w^*$-closed bimodules when $G$ has the approximation property ($AP$), a class of groups that includes all amenable and weakly amenable ones. As an application, we prove a version of Mercer's extension theorem for certain $w^*$-continuous isometric maps on $X$. We establish a similar theorem for bimodules arising from regular inclusions of finite factors, which generalizes the crossed product situation when $G$ acts on a finite factor. In the final section we apply these ideas to provide new examples of singly generated finite factors." @default.
• W1517553774 created "2016-06-24" @default.
• W1517553774 creator A5060764093 @default.
• W1517553774 creator A5063419044 @default.
• W1517553774 date "2014-01-14" @default.
• W1517553774 modified "2023-09-27" @default.
• W1517553774 title "Bimodules in crossed products and regular inclusions of finite factors" @default.
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• W1517553774 hasPublicationYear "2014" @default.
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