For an operator T which is a
quasi-affine transform of a subnormal operator S, we show that: (1) if S∗ has no
point spectrum and f : λ↦(T − λ)−1x is defined on an open set Ω, then there is a
dense subset Ω0 of Ω such that f∣Ω0 is analytic; and (2) if Σ is a spectral set of T
and Q is a peak set of R(Σ), then the spectral manifold XT(Q) is a reducing
subspace of T and Q is a spectral set of T∣XT(Q).