Is it possible to bypass one specific view for authentic users? I have a specific view. This is running well under admin rights but not with specific other roles which do not have the permission “Bypass content access control” 

Debugging with devel tools and related blocks as well as change permissions setttings in the role is not solving the problem :-(

Is there a easy way to create the possibility to give this specific view a "Bypass this view only for authentic users" ?
Under Advanced>Other>Query Settings, try checking Disable SQL rewriting.