Geodesic
Cohomology of groups in unitary representations, the neighborhood of the identity, and conditionally positive definite functions
Sbornik. Mathematics, Tome 47 (1984) no. 2, pp. 513-526

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It is shown that every irreducible unitary representation of a locally compact separable group with nontrivial first cohomology is unseparable from the identity representation in the space of irreducible unitary representations. For compactly generated groups the statement can be sharpened: a nontrivial cocycle in such a representation is in a certain sense the limit of trivial cocycles in irreducible representations. A survey is given of the connections between the notions indicated in the title. Bibliography: 17 titles. 
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     author = {A. M. Vershik and S. I. Karpushev},
     title = {Cohomology of groups in unitary representations, the neighborhood of the identity, and conditionally positive definite functions},
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A. M. Vershik; S. I. Karpushev. Cohomology of groups in unitary representations, the neighborhood of the identity, and conditionally positive definite functions. Sbornik. Mathematics, Tome 47 (1984) no. 2, pp. 513-526. http://geodesic.mathdoc.fr/item/SM_1984_47_2_a13/