The resolution 1024x768 (60Hz) works quite well. The image is stable and easy to read. However, the colors are not very brilliant and there are already blurring. If you look at a video (eg from Tageschau.de), so the quality is quite OK.
Good solution is also able to pass the audio signal from the headphone output of the computer to HDMI. It hums quite easily, but that I would be attributed to the cable or the computer.
Although Resolution 1920 & 1080 (60Hz) can be selected, but the picture is so bad that it is not useful.
Texts are to be read only with difficulty.
In the resolution 1360x768 (60Hz), the TV reports that the video signal is incorrect. The screen is blank (= blue).
The TV is a bit more than 1 year old, so maybe the HDMI implementation of the TV with guilt. However, I'm a bit disappointed that I can use the adapter only to 1024x768.
The program xrandr (Linux) reports at different resolutions not as 60Hz refresh rate, special values such as 59.8 Hz. Do not know if that indicates a weakness of the hardware.