ps tem -U e -u opções para isso.
De man ps :
-U userlistSelect by real user ID (RUID) or name. It selects the processes whose real user name or ID is in the userlist list. The real user ID identifies the user who created the process, see getuid(2).
-u userlistSelect by effective user ID (EUID) or name. This selects the processes whose effective user name or ID is in userlist.