  For R a bounded triply connected domain with boundary consisting of disjoint
Jordan loops there exists an operator T on a complex Hilbert space H so that
the closure of R is a spectral set for T, but T does not dilate to a normal
operator with spectrum in B, the boundary of R. There is considerable overlap
with the construction of an example on such a domain recently obtained by
Agler, Harland and Rafael using numerical computations and work of Agler and
Harland.
