  This paper extends the concept of Laplacian filtered quasi-Helmholtz
decompositions we have recently introduced, to the basis-free projector-based
setting. This extension allows the discrete analyses of electromagnetic
integral operators spectra without passing via an explicit Loop-Star
decomposition as previously done. We also present a fast scheme for the
evaluation of the filters in quasi linear complexity in the total number of
unknowns. Together with the fact that only a logarithmic number of these
filters are required for solving the h-refinement breakdown of electric field
integral equation, this results in an effective preconditioner that rivals
Calder\'on strategies in performance without relying on barycentric
refinements. Numerical results confirm the theoretically predicted behavior and
the effectiveness of the approach.
