Have a “Space” data type and an “Invited User” data type.
The user creates the spaces, and adds email addresses of the people they want to invite. You add these into the “Invited User” table = email address and the relevant Space.
Ping an email to all the addresses, asking them to login.
On the signup page, check to see if the entered email address is already on the “Invited User” page. If it is then as part of the login set them up so they can edit the space. Then delete the pending invite.
Examples above are slightly more complex, as you can be invited to multiple groups before signup.