On property (T) for pairs of topological groups

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Rigidity results for Bernoulli actions and their von Neumann algebras (after Sorin Popa) (2006, background): “le group does not have an inﬁnite subgroup with the relative property (T). Below, we need the following alternative characterization of relative property (T) due to Jolissaint (see Theorem 1.2(a3) in [30]). The pair (G,H) has the relative property (T) if and only if every unitary representation of G”
RELATIVE KAZHDAN PROPERTY (2005, background): “ (W,η)-invariant vector, πhas a (X,ε)-invariant vector. Given G,X,W,ε, if such η>0 exists, we say that Wis a ε-Kazhdan subset for (G,X). The following result generalizes a result due to Jolissaint [Jol] when X is a subgroup. Theorem 2.2.3. Let Gbe a locally compact group, and let X⊂ Gbe a subset.”
Cocycle and orbit equivalence superrigidity for malleable actions of w-rigid groups (2005, background): “the usual property (T) of Kazhdan for Γ ([K]). It is easy to see that if H = Γ, more generally if H is normal in Γ, then the ﬁxed vector ξ0 in (4.1.1) can be taken close to ξ. This fact was shown in ([Jo]) to hold true for arbitrary (not necessarily normal) inclusions H ⊂ Γ with the relative propert”
On Popa's Cocycle Superrigidity Theorem (2006, background): “For the general case of an arbitrary subgroup H < G with relative property (T), a different argument is needed (see [17], or the appendix in [21]).”