  We provide a systematic way to design computable bilinear forms which, on the
class of subspaces $W^* \subseteq \mathcal{V}'$ that can be obtained by duality
from a given finite dimensional subspace $W$ of an Hilbert space $\mathcal{V}$,
are spectrally equivalent to the scalar product of $\mathcal{V}'$. Such a
bilinear form can be used to build a stabilized discretization algorithm for
the solution of an abstract saddle point problem allowing to decouple, in the
choice of the discretization spaces, the requirements related to the
approximation from the inf-sup compatibility condition, which, as we show, can
not be completely avoided.
