  Following work by Casazza, Kutyniok and Lammers, and extensions by Stoeva and
Christensen, we provide some novel characterizations of R-dual sequences of
type III in Hilbert spaces. We systematically extend the construction procedure
by basing it on a choice of an antiunitary involution. For certain classes of
R-duals of type III, we derive a representation of the associated frame
operator in terms of spectral measures.
