Ricerc@Sapienza

Given an action ? of a discrete group G on a unital C?-algebra A, we
introduce a natural concept of ?-negative definiteness for functions from G to A,
and examine some of the first consequences of such a notion. In particular, we prove
analogs of theorems due to Delorme–Guichardet and Schoenberg in the classical case
where A is trivial. We also give a characterization of the Haagerup property for the
action ? when G is countable.