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- W4290000008 abstract "Three separation properties for a closed subgroup $H$ of a locally compact group $G$ are studied: (1) the existence of a bounded approximate indicator for $H$, (2) the existence of a completely bounded invariant projection of $VNleft(Gright)$ onto $VN_{H}left(Gright)$, and (3) the approximability of the characteristic function $chi_{H}$ by functions in $M_{cb}Aleft(Gright)$ with respect to the weak$^{*}$ topology of $M_{cb}Aleft(G_{d}right)$. We show that the $H$-separation property of Kaniuth and Lau is characterized by the existence of certain bounded approximate indicators for $H$ and that a discretized analogue of the $H$-separation property is equivalent to (3). Moreover, we give a related characterization of amenability of $H$ in terms of any group $G$ containing $H$ as a closed subgroup. The weak amenability of $G$ or that $G_{d}$ satisfies the approximation property, in combination with the existence of a natural projection (in the sense of Lau and Ulger), are shown to suffice to conclude (3). Several consequences of (2) involving the cb-multiplier completion of $Aleft(Gright)$ are given. Finally, a convolution technique for averaging over the closed subgroup $H$ is developed and used to weaken a condition for the existence of a bounded approximate indicator for $H$." @default.
- W4290000008 created "2022-08-06" @default.
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- W4290000008 date "2017-03-08" @default.
- W4290000008 modified "2023-09-23" @default.
- W4290000008 title "Weak separation properties for closed subgroups of locally compact groups" @default.
- W4290000008 doi "https://doi.org/10.48550/arxiv.1703.02909" @default.
- W4290000008 hasPublicationYear "2017" @default.
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