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We show that if $M\,\bar{\rtimes }_{\unicode[STIX]{x1D6FC}}\,\unicode[STIX]{x1D6E4}$ has the weak Haagerup property, then both $M$ and $\unicode[STIX]{x1D6E4}$ have the weak Haagerup property, and if $\unicode[STIX]{x1D6E4}$ is an amenable group, then the… Click to show full abstract
We show that if $M\,\bar{\rtimes }_{\unicode[STIX]{x1D6FC}}\,\unicode[STIX]{x1D6E4}$ has the weak Haagerup property, then both $M$ and $\unicode[STIX]{x1D6E4}$ have the weak Haagerup property, and if $\unicode[STIX]{x1D6E4}$ is an amenable group, then the weak Haagerup property of $M$ implies that of $M\,\bar{\rtimes }_{\unicode[STIX]{x1D6FC}}\,\unicode[STIX]{x1D6E4}$ . We also give a condition under which the weak Haagerup property for $M$ and $\unicode[STIX]{x1D6E4}$ implies that of $M\,\bar{\rtimes }_{\unicode[STIX]{x1D6FC}}\,\unicode[STIX]{x1D6E4}$ .
Journal Title: Bulletin of the Australian Mathematical Society
Year Published: 2017
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