Calendar sharing & event invites not working (neither iCloud.com nor through the iCal app)

Hello everyone

I created a new iCloud account with a brand new Apple ID. In order to use the calendar I had to set up that account in the iCal app on my iMac.

Now I would like to share my calendar with others. I tried that on icloud.com and in the iCal app by entering the email address of another icloud user in the share options of my calendar. I tried multiple addresses but none of them receive any email. The entered address disappears after I re-open the share window.

The same thing happens when I try to invite someone to an event. Nobody does get an email or a notification. It seems that my account is somehow not able to send out emails.

I tried to set up the icloud email address for my account but with no success.

Strangely enough it works fine with an older account and with the accounts of my colleagues.

Does anyone has an idea what can be the cause of this? It's rather annoying...

Any tip is highly appreciated.