Trump, who is feuding with US allies around the world, needs to show he can master the diplomatic formalities that govern US relations with a region where tradition and symbolism are particularly important parts of power relationships and regional rivalries threaten the peace.
Abe is seeking to forge a personal bond with Trump that would surmount Japanese fears about his critical campaign trail rhetoric and reaffirm the US guarantees crucial to Japanese security as China asserts itself and North Korea threatens aggressive steps.
To some degree, both leaders will be looking to reassure each other after a rocky start dating from Trump's days on the campaign trail -- the American President that he values the relationship and the Japanese Prime Minister that there is value in the relationship.
Trump repeatedly launched broadsides against Tokyo, which he has accused of taking US jobs, and rattled the Japanese public by suggesting the country contemplate going nuclear and stop relying on the US for defense. "You know we have a treaty with Japan where if Japan is attacked, we have to use the full force and might of the United States," he said in August. "If we're attacked, Japan doesn't have to do anything. They can sit home and watch Sony television, OK?"
Now Trump, after fractious encounters with the leaders of US allies Mexico and Australia, has a chance to improve his image on the world stage through Abe's visit.
'Dispelling any doubts'
An administration official said the President will work to reassure Japan of the US commitment following Defense Secretary James Mattis' trip to the region, his first in office, last week.
On that visit, he reaffirmed Washington's treaty commitment to defending Japan, which has charged territorial disputes with China, and its intention to continue to station US troops there, despite Trump's criticism of the practice while a candidate.
"You're going to to hear similar messages from the President himself and that will go a long way toward dispelling any doubts that remain," the official told CNN.
Indeed, that affirmation was exactly what Abe wanted to hear, a Japanese official said. "We were all very happy and appreciate the positive message Defense Secretary Mattis sent while in Japan," the official said. "We needed these assurances."
In fact, they helped defuse the tweets put out by Trump.
"We are trying not to react to each and very tweet the President and his staff (send) out," the official said. "We have gotten reassurances from Mattis, who is very well-trusted and he is acting on behalf of the President, and that shows our relationship is strong and we should not be fooled by the messages coming out of Washington."
Review and reaffirm the relationship
Abe, for his part, will try to clarify what is seen as an outdated White House impression of Japan and tout the country's economic contributions to the US, as well as elicit a reaffirmation of Washington's security commitments.
"I think that with this summit they'll both aim to project a sense of a strong and productive alliance," said Matthew Goodman, a senior chair in political economy at the Center for Strategic and International Studies.
Japanese officials said Abe will use the opportunity to review Tokyo's sense of regional threats and go over trade and investment to make clear that Japan creates and sustains US jobs, including 1.5 million in the auto industry. "Our aim is to review and reaffirm the current relationship," the official said.
And he might be most successful in making his points on the golf course Saturday, after the more traditional day of diplomacy on Friday, including a bilateral meeting, news conference and working lunch.
Both men are avid golfers and Trump's invitation to Abe to join him at the "winter White House" on his Ma-a-Lago resort in Florida represents a significant coup for the Japanese Prime Minister. It's being taken as a huge personal compliment by Abe and may go some way toward easing Tokyo's concerns about Trump.
The Japanese leader has gone to extraordinary lengths to forge personal ties with Trump, hoping that a friendship will solidify the US-Japan security partnership. Abe made strenuous efforts to reach out to Trump after his election, an initiative that yielded a meeting in Trump Tower with the President-elect, his daughter Ivanka and her husband, Jared Kushner. There, Abe presented Trump with brand new driver with a golden head.
This time, "Abe will be bringing omiage," said Goodman, referring to the traditional Japanese practice of gift-giving, "but in a big way."
Indeed, Abe may bring with him a package of Japanese investments in US infrastructure, including high speed rail and new investment in municipal bonds to finance infrastructure and construction that would create US jobs, according to Goodman and officials. Abe may also raise the prospect of Japan buying more US energy.
"It's a way of getting to what Abe really cares about: making sure the US has Japan's back," especially given China's assertiveness, Goodman said. Any economic package "will ultimately be designed to win Trump's understanding for a stronger alliance."
Setting the record straight
Another of Abe's missions will be to update Trump's vision of Japan. The Prime Minister wants to counter "some of the rhetoric circulating in the Trump administration" about Japanese burden sharing, currency manipulation and other misconceptions, the Japanese official said, adding, "Japan is the US' number one trade partner in Asia. We need to set the record straight."
Goodman pointed out that Japan no longer intervenes in currency markets to suppress the value of the yen and invests heavily in the US, with automakers supporting about 1.5 million jobs.
"Job one for Prime Minister Abe will be to try to update President Trump on the realities, as well as the fact that Japan is a somehow not ungrateful ally who hasn't contributed enough," Goodman said.