  In recently proposed stabilisation techniques for parabolic equations, a
crucial role is played by a suitable sequence of oblique projections in Hilbert
spaces, onto the linear span of a suitable set of M actuators, and along the
subspace orthogonal to the space spanned by the first M eigenfunctions of the
Laplacian operator. This new approach uses an explicit feedback law, which is
stabilising provided that the sequence of operator norms of such oblique
projections remains bounded. The main result of the paper is the proof that,
for suitable explicitly given sequences of sets of actuators, the operator norm
of the corresponding oblique projections remains bounded. In the final part of
the paper we provide numerical results, showing the performance of the explicit
feedback control for both Dirichlet and Neumann homogeneous boundary
conditions.
