A pressure intensifier device increases pressure in a pressurized fluid chamber of a piston/cylinder unit. The pressure intensifier device has a pressure intensifier cylinder and a pressure intensifier piston, which is guided in an axially movable manner in the cylinder, wherein the pressure intensifier cylinder has an outlet region, an inlet region upstream of the outlet region and a piston guiding chamber, and the pressure intensifier piston has a piston part, which is guided in the piston guiding chamber, and a piston rod, which extends from the piston part to the inlet region, in a maximally retracted release position releases a fluid connection between the inlet region and the outlet region and, in a maximally advanced blocking position, blocks this connection with a free end portion, with which it extends into the outlet region. Over a portion that can be passed through by the free end portion of the piston rod during movement from the release position into the blocking position, the outlet region has a free passage cross section for the free piston rod end portion that is at least equal in size to a rod cross section of the free piston rod end portion. A pressure intensifier inlet valve can be controlled independently of a pressure in the pressurized fluid chamber of the piston/cylinder unit.