[Update] Split-screen looks to be available, just not the ability for two people to log into the game with two separate PSN IDs to gain Trophies and stats. It would seem that only one player can do it, which is a bummer. Still, that's great news for the state of split-screen in the game. Thanks to all of the comments below for the clarification.
Matt Charles, Producer of Borderlands 2, upon receiving a plethora of questions from fans after revealing the Collector's Editions for the title (as reported by Keri earlier), have answered many of them in an official response on PlayStation's official blog.
Some of the answers are the usual fare of "Yes, we're improving everything so don't worry about anything and thanks for asking!", but a few of them reveal some interesting tidbits.
First and foremost, local splitscreen is currently off the table but that's only for now. The original Borderlands had splitscreen, so hopefully it's placed back in, though the loss of local splitscreen is nothing new and spurred on by the developer and publisher wanting more people to purchase copies of the game. [See update]
For combat, health kits have been thoroughly removed in the place of new relics and shields, so that combat isn't interrupted by having to open the inventory to recover health. Also making the combat more fluid, money and ammo will automatically be picked up.
Luckily, voice communication should be fixed, avatar customization will be improved with swappable heads and hairstyles, and a four-player vehicle called the Technical will have customizable weapon configurations. The level cap returns to 50 as it was in Borderlands before the DLC, but you never know... it could jump back to 69.
Finally, if you pre-order Borderlands 2, the Mechromancer class will be free once it's available through the Borderlands 2 Premiere Club. It will also detect whether players have a save file from the first Borderlands, and award them with swappable head and skin for every class. Borderlands 2 releases on September 18th.