Is there a relationship between the mass of a SMBH and the kinetic energy of its host elliptical galaxy?

We use a restricted sample of elliptical galaxies, whose kinematical parameters inside the semi-major axis were calculated correcting for the effect of the integration of the light along the line of sight, in order to analyze a possible relationship between the mass of a supermassive black hole (SMBH) and the kinetic energy of random motions in the host galaxy. We find M-BH proportional to (M-G sigma(2))(alpha) with 0.87 <= alpha <= 1 depending on the different fitting methods and samples used. This result could be interpreted as a new fundamental relationship or as a new way to explain the old M-BH-sigma law. In fact, the relations of the velocity dispersion both with the mass of the SMBH (M-BH proportional to sigma(4.12)) and with the mass of the host galaxy (MG proportional to sigma(2.16)) induce us to infer an almost direct proportionality: M-BH proportional to M-G sigma(2). A similar relationship is found for the total kinetic energy involving the rotation velocity too.