The ignition of a gas discharge lamp is followed by a warm-up phase. During warm-up, sufficient power must be converted to enable the lamp to transition to an operating phase. This causes currents flowing at a damaging level into the electrodes in known devices. These high currents are avoided using: a regulation device that regulates the power of connected gas discharge lamps to a desired power; a setting device that limits a lamp current of connected gas discharge lamps to a limit value; a detection device that outputs a signal to the control device if a limit value setting is too low, putting a connected lamp into a state in which the lamp assumes the desired power; and a control device prescribing the limit value for the setting device and increasing the limit value if the detection device sends a signal to the control device.