Others have replied on this, with good advice, but I'll throw in mine,
with a warning of consequences.

If postinngs from nonsubscribers and new subscribers must be approved
you have that covered (unless the person is savvy enough to forge mail
so it goes through regardless).  If the net-kook is getting other
subscribers to forward/post the items on her behalf, you simply announce
that anyone who does so will be placed on review for cause, repeated
attempts constitute grounnds for list banishment.

Now, be aware that with a dedicated net-kook you may keep his postings
from reaching your list, by whatever means.  However, the kook my then
adopt different tactics:

Character asassination of you on related (not yours) lists

The dedicaated kook may track down where you live, your phone number,
where you work, your phone number there, where your spouse works,
where your kids go to school, etc.

Now the kook gives you no rest day or night.  All out effort will be
made to destroy your sanity, your family, your job.

Some listowners have killed their lists rather than suffer this torture.

Some have put their list on hold for six months or so, to let things
quiet down and *maybe* the kook will go away.

Some, despite the most violent attacks, have stuck it out, been supported
by their employers and the host of their lists, and have won in court
(the kook never shows up to prosecute his civil suit and never responds
to your counter suits, you win by default).  However, the extreme stress
of the situation may result in a "nervous breakdown" requiring
professional counseling and may strain your family, job, everything
to the breaking point.

Do NOT reply to the harrassing items from the kook, don't even read
them, they'll just increase your stress.  However, SAVE them.  Save
everything relating to the problem!!

DOCUMENTAION!   RECORDS!   ARCHIVES!

You must have UNALTERED records to support your case!

All listowners must live with the realization that personal assault by
a net-kook due to the list is a possibility.  Most of them will tire of
the game if you quietly block their postinngs and ignore their ravings.
But there's always the chance of a dedicated net-kook, who truly will
"make a federal case out of it."  Documentation!  Records!  Archives!

Douglas