  In a previous paper the author constructed biinvariant measures (possibly
having values in a line bundle) for a loop group LK (with compact simply
connected K) acting on the formal completion of its complexification LG. One
motivation for this was to find a geometric construction for the unitary
structure for the positive energy representations of LK. In this paper we
pursue an analogous construction for the group of diffeomorphisms of the
circle.

Functional Analysis;Operator Algebras