US perception of Okinawa during and immediately after WW2, any books I can read on this topic?

In particular I want to know if the Americans viewed the Okinawans as Japanese, Chinese (apparently, according to Nakayoshi Ryoko…) or something entirely else. Okinawa and Japan's southernmost territories is probably the only piece of land in Japan that could have ended up in someone else's hands depending on how the cold war progressed, but I just can't find a lot of studies on this. Not many people talk about how the US perceived the islands' sovereignty.