  We investigate the linear stability of inviscid columnar vortices with
respect to finite energy perturbations. For a large class of vortex profiles,
we show that the linearized evolution group has a sub-exponential growth in
time, which means that the associated growth bound is equal to zero. This
implies in particular that the spectrum of the linearized operator is entirely
contained in the imaginary axis. This contribution complements the results of a
previous work, where spectral stability was established for the linearized
operator in the enstrophy space.
