Abstract
We have seen that, if a locally compact group G contains a closed noncom-pact subgroup H such that the pair (G, H) has relative property (T), then G may not have the Haagerup property. Hence we may ask whether relative property (T) (with respect to a noncompact subgroup) is the only obstruction to the Haagerup property. It was proved in Theorem 4.0.1 that the answer is positive for connected Lie groups1.
Article Footnote
1S.Popa suggested that, at the philosophical level, our question is analogous to von Neumann’s question: “Is the presence of a free nonabelian subgroup the only obstruction to amenability?”... and that both questions might share the same odd fate!
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© 2001 Springer Basel AG
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Valette, A. (2001). Open Questions and Partial Results. In: Groups with the Haagerup Property. Progress in Mathematics, vol 197. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8237-8_7
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DOI: https://doi.org/10.1007/978-3-0348-8237-8_7
Publisher Name: Birkhäuser, Basel
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