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WEAK HAAGERUP PROPERTY OF
$W^{\ast }$-CROSSED PRODUCTS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 97 / Issue 1 / February 2018
- Published online by Cambridge University Press:
- 31 August 2017, pp. 119-126
- Print publication:
- February 2018
-
- Article
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- You have access
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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 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 
$M\,\bar{\rtimes }_{\unicode[STIX]{x1D6FC}}\,\unicode[STIX]{x1D6E4}$.
