The Washington Post is being optimistic; it's claiming "Hopes for Peace Diminished in the wake of Abbas' resignation.
I don't share that view; I'm sadly of the opinion that they're pretty much over and done with. I was of that opinion when I heard that Abbas resigned, and it was only confirmed with the immediate (and unsuccessful) attack on Hamas founder Sheikh Yassin, which will be an unmistakable signal to all concerned of exactly how things are going to go. (Of course, the bus bombing of last week was a pretty clear signal itself.)
So, in the words of Bugs Bunny, "this means wah". Israel's talk about expelling Arafat will likely come to pass , and I have little faith that the Palestinian Authority will survive him with Abbas gone. Without the Authority, the Israelis will have little choice but to take over regional administration themselves; the West Bank will devolve into out-and-out chaos otherwise, unless Hamas takes control.
Israel's attempt to try to control the Palestinians will be difficult at best, more likely impossible; obedience is required for control, and there is little chance that the Palestinian population will be at all obedient to the Israeli army. The violence will get worse, rather than better, as Palestinians attack Israeli soldiers and civilians at every opportunity and the increasingly frustrated Israeli army cracks down to repress the violence. All the while, peacemakers will lose power, and extremists will gain it, pointing at the acts of "the other side" (while conveniently minimizing their own) in order to justify more and more radical responses.
I suspect I know where this is going. I don't like it. But I'm starting to wonder if it's even possible to stop it.