If you see the above image, then yes PSN is back.
The above image shows the heat map (or number of players playing, in graphic form) for Call Of Duty: Black Ops players in North America. At 05/14/2011 12:00 AM Pacific Time, Sony brought back the PlayStation Network, much to the chagrin of the many players who’ve waited since Sony shut down the servers following the attack on April 20th. About 4 weeks have passed, and while gamers have had to endure the harshness of the offline world, knowing that it is back online and running (in North America, at least) is reassuring to many.
And while much blame has been thrown to Sony for not protecting thier users from the malicious attack perpetrated by unknown parties, Sony has been adamant to support gamers by giving them free access to PSN Plus, free games, and reimbursements for those subscribed to services such as Qriocity and various MMORPG games hosted by Sony.
The damage has been dealt, but it seems that Sony now has to bring things back to normal. Whether or not gamers can trust them is still an open question that will only be answered in the future. All that remains now is that pro-gamers can start resuming thier matches online, after a harrowing downtime.