Part of the problem is, who is the "user".

Under WinnT, scheduled backups generally run under the System account.  Any
USER account may or may not be logged on at the time backups are run.  On
UNIX, the backups generally run as root.

What we do is query the eventlog on the server end, and generate mail
messages to be sent to users whose backups fail or miss.  That works if you
have a way to map the TSM node names into mail ids.  But, it doesn't take
into account any individual files that fail to back up, we really don't have
a solution for that yet.