Most elliptical galaxies contain central black holes (BHs), and most also contain significant amounts of hot gas capable of accreting on to the central BH due to cooling times short compared to the Hubble time. Why therefore do we not see AGNs at the center of most elliptical galaxies rather than in only (at most) a few per cent of them? We propose here the simple idea that feedback from accretion events heats the ambient gas, retarding subsequent infall, in a follow up of papers by Binney & Tabor (1995, BT95) and Ciotti & Ostriker (1997, CO97). Even small amounts of accretion on a central BH can cause the release of enough energy to reverse the central inflow, when the Compton temperature (T X ) of the emitted radiation is higher than the mean galactic gas temperature, the basic assumption of this paper. Well observed nearby AGN (3C 273, 3C 279), having T X near 5 × 10 8 K, amply satisfy this requirement. In this context, we present a new class of 1D hydrodynamical evolutionary sequences for the gas flows in elliptical galaxies with a massive central BH. The model galaxies are constrained to lie on the Fundamental Plane of elliptical galaxies, and are surrounded by variable amounts of dark matter. Two source terms operate: mass loss from evolving stars, and a secularly declining heating by type Ia supernovae (SNIa). Like the previous models investigated by Ciotti et al. (1991, CDPR) these new models can evolve up to three consecutive evolutionary stages: the wind, outflow, and inflow phases. At this point the presence of the BH alters dramatically the subsequent evolution, because of the energy emitted due to the accreting gas flow. The effect of Compton heating and cooling, of hydrogen and helium photoionization heating, and of bremsstrahlung recycling on the gas flow are investigated by numerical integration of the nonstationary equations of hydrodynamics, in the simplifying assumption of spherical symmetry, and for various values of the accretion efficiency and supernova rates.The resulting evolution is characterized by strong oscillations, in which very fast and energetic bursts from the BH are followed by longer periods during which the