In this paper various triples of
operator-valued functions acting in a Hilbert space are characterized, and the
members are shown to be connected by a one-to-one-to-one correspondence. The
elements of the triples are operator measures, generalized resolvents, and positive
definite sequences which are related to the unit circle. The relationships between
operator measures and positive definite sequences were first obtained by M. A.
Naǐmark and B.Sz.-Nagy in their dilation and moment theorems. The main
contribution of this paper is a characterization of the interrelated resolvent classes.
By exploiting the correspondence between the various classes, a unified development
of the theory is obtained.
