We appreciate you checking on that for us, Ralf,
Are you able to connect your TV via AirPlay? This article will show you how to do so: Use AirPlay to stream what’s on your Mac to an HDTV - Apple Support
1. Make sure your Mac and Apple TV are on the same network.
2. Click Control Center
in the menu bar, click the Screen Mirroring icon
, then choose your Apple TV.
3. If asked, enter a four-digit code on your Mac.
4. To set whether your desktop mirrors or extends your Mac screen, click the Screen Mirroring icon
, then choose Mirror Built-in Display or Use As Separate Display.
Is it that your TV doesn't see your Mac desktop? Is the display just blank?
Any specific details about the behavior you're experiencing can help us to isolate this behavior further.
We look forward to your reply.
Cheers!