someone from the building where I own a co-op apartment posted a
notice acused me, by using my name and my apartment number, of being
meddlesome, irrational, lies and harasses people. And also, encourages
me to leave. Isn't the fact that this notice was taped to all 6
floors, my apartment door and the laundry room,considered defamation
of character and if so, what do you suggest? Thank you
whomever posted this not

Keeping in mind that this forum cannot dispense legal info, it sure
seems that this is defamatory. State laws differ on this matter so
knowing where you live would help a Researcher answer your question.

Personally, I'd take the person to small claims court. You'll need
witnesses who got the notice to describe how it has diminished their
opinion of you.

However, it is only defamatory if the allegations are untrue. If ever
the case came to court you would have to defend yourself because the
plaintiff would clain that they were true.
I would save a copy of the document and try to find proof of
authorship. Then consult a lawyer. But I suspect that legal costs
would be high. Try to rise above noticing such trivia, if at all
possible.

Search in the box below for:   defamation

You will find a several questions and answers (8 since August and
about 86 in total).
Perhaps these can help you.

Amber and Richler-- Small claims costs are very low. And sure, the
allegations need to be pretty much false but the method the person
used to promulgate the accusations smacks of harrassment and bias.
Such a defendant would be on shaky ground to start with in court.
Furthermore, while the argument that this is protected speech could be
made, it would certainly be disallowed.

If you want to go that route, this book might help:
http://www.nolo.com/product.cfm/objectID/EE829024-37B3-4FA5-A32D6DCEF421A1A5/toc/1/104/

It sounds like this person might be difficult to deal with, but it
would be nice if you could find out what the problem is and perhaps
resolve it without resorting to the courts.  Even if you were to win a
judgement, you would still have to live in the same building with this
person, who would then be utterly convinced in their opinion of you.