With a new Palestinian leader in place, all eyes are now on the kind of relationship Israel will form with him. Israeli Prime Minister Ariel Sharon has said Mahmoud Abbas is a man Israel can do business with. But concessions will be necessary on both sides if the relationship between Israel and the Palestinians is to improve, says BBC Middle East reporter Lucy Williamson.
Mahmoud Abbas may be someone Israel can talk with
There is a mood of cautious optimism drifting across the state of Israel.
You can see it here and there in the newspaper columns, hear it in the odd coffee shop conversation.
After four decades of Yasser Arafat, there is hope among some Israelis his death in November will mark a new era in relations with the Palestinians.
Mr Sharon has already signalled his willingness to talk to Mahmoud Abbas, after years of sidelining his predecessor. Mr Abbas has said he is willing to talk to Mr Sharon.
The new Palestinian leader has also spoken out against the armed intifada, saying it has damaged the Palestinian nation, something that has gone down well with many Israelis.
But others are more sceptical.
Like some of their Palestinian counterparts, who believe Israel will never deliver on its promises to any Palestinian leader, there are those in Israel who say nothing will change with Mahmoud Abbas.
They point to his election campaign, when he spent time with militants in the West Bank town of Jenin, and to his comments, after the killing of seven young people in Gaza, when he referred to Israel as the "Zionist enemy".
It is certainly true that Mahmoud Abbas has a difficult task ahead to keep the array of Palestinian political factions on board while he negotiates with Israel.
But it is not all down to Mr Abbas.
Israel too will need to make concessions, and gestures of good faith, to strengthen Mr Abbas's hand with his own people. The question is whether the majority of Israelis are prepared to do so.
One move sure to win Palestinian confidence would be to ease travel restrictions within the Palestinian territories. But many in the Israeli government say Mr Abbas will need to act first, by cracking down on militants.
Another gesture that would go down well with the Palestinians would be to involve their new leadership in Mr Sharon's plan to withdraw all Jewish settlers from Gaza in the coming year.
But it is a gesture that may not go down so well in Israel. Some on the political right in Israel are already angry at the plans, which they see as "giving in to terrorism". Co-ordinating the withdrawal with the Palestinians would be seen by them as an even greater defeat.
For the last few years of Mr Arafat's premiership, Israel refused to have any contact with him, accusing him of failing to crack down on militants it said were responsible for attacks against Israeli targets.
It may well prove easier for Israel to draw up a chair at the negotiating table opposite Mahmoud Abbas.
But the end game remains the same - what to do about the key final status issues like the rights of Palestinian refugees to return to their former homes, the borders of a Palestinian state, the expanding Jewish settlements in the West Bank and the status of East Jerusalem.
Mr Abbas will find it just as hard as Mr Arafat to sell any concessions on these issues to either the politicians, or the people back home.