Short and sweet: A converter was needed. First attempt: An HDMI to VGA and composite converter. However, this unfortunately gave a 1: 1 output resolution, what I noticed too late, the output was not scalable and therefore can not be displayed on the TV. So I sent the converter being returned to sender. Since the HDMI VGA Converter not exist at this time with scalable resolution just, I ordered also by LIGAWO an HDMI to HDMI Converter with abkoppelbarem sound (via RCA and Toslink). Even this did not work as expected, either only the faded image on HDMI TV has been displayed, but no sound despite this routing the signal to the AV receiver or I heard parallel, upon deactivation of the HDMI output only the sound. So device returned by return mail.
Now, after some desperation there have finally the HDMI to VGA converter with scalable output resolution with disconnection of the sound signal works (over 3,5er jack) and this time it has: The converter reckoned the HDMI signal properly on a VGA output resolution of 1280 x 1024 pixels down, provides for VGA ratios a razor-sharp, high-contrast image and the sound is running, if a little quiet, at the same time correctly on the AV receiver. Considering the cost of a new television and the fact that my TV for my circumstances do not yet as old and some time would be used, I've made with the purchase of this converter a great business, because now I have to not specially buy a new television for modern HDMI devices.
CONCLUSIONS: Absolute buy recommendation for those who want to operate eneuere HD devices to an old projector or TV with VGA connection!