  The past two decades have seen a revolution in ab initio calculations of
nuclear properties. One key element has been the development of a rigorous
effective interaction theory, applying unitary transformations to soften the
nuclear Hamiltonian and hence accelerate the convergence as a function of the
model space size. For consistency, however, one ought to apply the same
transformation to other operators when calculating transitions and mean values
from the eigenstates of the renormalized Hamiltonian. Working in a
translationally-invariant harmonic oscillator basis for the two- and
three-nucleon systems, we evolve the Hamiltonian, square-radius and total
dipole strength operators by the similarity renormalization group (SRG). The
inclusion of up to three-body matrix elements in the 4He nucleus all but
completely restores the invariance of the expectation values under the
transformation. We also consider a Gaussian operator with adjustable range and
find at short ranges an increased contribution from such induced three-body
terms.
