If the mail(); function i corectly written i send you mail like a normal from a client, over the SMTP server you just add'ed (you know that!).
There is some mail providers there by dafualt have disablet to delevery for mails, with a not legal mail address:
e.g.
Ant Michael (not vaild!), michael@firm.com (vaild!)
systems like this often just work with a "@" check, if a "@" is found in the string, the mail is vaild!