WASHINGTON - It was supposed to be Prime Minister Ehud Olmert's big comeback. A shot with U.S. President George W. Bush in the Rose Garden, an image that would lead all Israeli television viewers to realize that Olmert has come out of the crisis and that his leadership has been accepted anew by the president of the most important world power.

But this week will be remembered not for Olmert's comeback, but for that of Palestinian Authority Chairman Mahmoud Abbas - the same Abu Mazen whose weakness was a source of laughs for Israeli officials, the same Abu Mazen who lost almost half the Palestinian Authority just last week, the same Abu Mazen who recently called off his meeting with Olmert in anger. That same Abu Mazen has suddenly become the object of Israeli and American hopes.

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Since landing in the United States, Olmert's delegation has depicted Abbas as the last bulwark keeping out the flood of Islamic fundamentalism and preventing Hamas from getting a foothold in the West Bank. The Hamas takeover of the Gaza Strip caught Israel unprepared, although it shouldn't have surprised anyone.

Israel's initial reaction was confused, and dealt with the deployment of an international force in Rafah, as though any country wants to send its troops to clash with a well-organized and well-armed terrorist movement. Only a few days later did Olmert provide a different response: The Hamas victory in Gaza is an achievement for Israel, because it creates the opportunity to hold talks with the friendly Fatah government in the West Bank, and breaks the political freeze that resulted from the embargo of the Hamas government.

Washington was no less surprised by the Hamas takeover. In America too, administration officials attempted to turn the fall of another Middle East outpost to the hands of an Islamic organization with close ties to Iran into a diplomatic victory.

Once again, the buzzwords are "breakthrough" and "great opportunity," not to mention "political horizon" regarding the establishment of a Palestinian state - even if one of its arms has been cut off.

The problem is that the basic conditions have not changed. Abbas does not control contiguous territory, since the Palestinian enclaves in the West Bank are under Israeli military control. Renewed funding from the United States and Europe doesn't guarantee Abbas public support from the Palestinian people.

It's tough to envision Abbas suddenly bringing order to the territories. It's also tough to envision Israel showing a generosity that goes beyond declarations or marginal steps like unfreezing Palestinian funds. And the Hamas takeover of Gaza has diminished the possibility that Israel will withdraw from additional territory.

Under these conditions, Abbas' comeback is likely to be short-lived, just as it was in the past. Aas the events in Gaza demonstrated, Abbas, Olmert and Bush are not alone on the playing field. They face devious and determined rivals - Iranian President Mahmoud Ahmadinejad, Syrian President Bashar Assad, and Hamas leaders Khaled Meshal and Ismail Haniyeh - who have doubtless read the reports from Washington on the "new American strategy," and are doubtless figuring out how to ruin it, as they did its predecessor.