NOVELTY - The apparatus (1) has an air compression system (2) provided with a vaned-rotor (11) and a volute (13), and an electric motor (3) driving the vaned-rotor. A ventilator (4) has a vaned-rotor (26) and a volute (21) which are reversely arranged with respect to the vaned-rotor (11). The volute (21) is directly connected to a cooling air transporting conduit (5), cooling air circulation passages (6) and a cooling air evacuation conduit (7) to distribute pressurized cooling air generated by the ventilator towards a foil air bearing assembly (17), an air thrust bearing assembly (18) and the motor.    USE - Gas compression apparatus i.e. turbo machine, for use as a pressurized air supply source for a fuel cell or use as a pressurized air generator in a ventilating system of a cabin of a vehicle i.e. aircraft, and for driving a turbocharger of the vehicle.    ADVANTAGE - The volute of the ventilator is directly connected to the cooling air transporting conduit, the cooling air circulation passages and the cooling air evacuation conduit to directly distribute pressurized cooling air towards the foil air bearing assembly, the air thrust bearing assembly and the motor, thus cooling the bearing assemblies and the motor in an optimal manner and in better conditions while avoiding utilization of an external cooling unit. The apparatus is simple, self-controlled, reliable and inexpensive. The usage possibilities and performances of the apparatus are increased, the encumbrance of the apparatus is reduced, and the energetic yield of the apparatus is improved. The apparatus reduces energetic impact on the air thrust bearing assembly.    DESCRIPTION OF DRAWING(S) - The drawing shows a longitudinal sectional view of a gas compression apparatus.    Gas compression apparatus (1)    Air compression system (2)    Electric motor (3)    Ventilator (4)    Cooling air transporting conduit (5)    Cooling air circulation passage (6)    Cooling air evacuation conduit (7)    Vaned-rotors (11, 26)    Volutes (13, 21)    Foil air bearing assembly (17)    Air thrust bearing assembly (18)