Now about Abe saying that he has established a relationship of trust with Trump, as many in the non-Japanese speaking news biz have reported, it is important to know exactly what the prime minister said after his meeting with the Trumps.
In prepared introductory remarks, the prime minister said this about trust:
共に信頼関係を築いていくことができる、そう確信の持てる会談でありました。中身につきましては、私は私の基本的な考え方についてはお話をさせていただきました。様々な課題についてお話をいたしました。
That we together could build a relationship of trust, we had a conversation that could confirm this. As for the internal details, he let me relate to him my basic way of thinking. I talked about a range of subjects.
In this opening statement Abe does not say that he trusts Trump. What he says is that he went into their conversation with a purpose of building a relationship of trust and that the president-elect allowed him to express his own views. As to what he thought of what Donald Trump said in the meeting, nothing.
It was in response to a reporter's question (smart reporter) that Abe had to make a second, unprepared statement about trusting Trump:
個別具体的なことについてはお答えできませんが、同盟というのは信頼がなければ機能しません。私は、トランプ次期大統領は正に信頼できる指導者であると、このように確信しました.
I cannot answer your question concretely as regards the views of each but without trust an alliance cannot function. As for me, as for whether or not President-Elect Trump is a leader one can truly trust, I was able to confirm this.
For me, the intrusion of the adverbials masa ni ("truly, really, actually") and kono yo ni ("in this manner") makes this response sing. These phrase hint that Abe is making a case rather than responding in earnest.
Thanks to the vagaries of Japanese sentence structure the PM never says he trusts the President-elect. What he says he has confirmed is whether or not he can truly trust him -- to which the answer is yes, he has confirmed it -- it being "whether or not he can truly trust him."
To which, if Abe is asked later by someone interested in what transpired in that first meeting, he can in all honesty reply:
Oh yes, I did confirm whether or not I could truly trust him, and the answer to that question was, "No, I could not."
So yes, Abe did confirm something about Trump and trust. But the door is open on just what that something is.
And that ambiguity is in everyone's interest right now.
Later - In comment, David Littleboy offers a possible and highly likely explanation of kono yo ni that would strengthen the case of those saying that Abe has declared Trump trustworthy.
The Japan News, which is translated from the pro-government Yomiuri Shimbun's reports, takes the circumspect route (Link).
The always problematic official-yet-only-provisional Prime Minister's Residence translation is, by contrast, emphatic (Link).