What a Muslim can or cannot do while fasting (in Ramadan) is explained in Quran (2:187).
There are people who may not fast in Ramadan, which is also explained in 2:184.
Now, in Ramadan, there will most probably be people who couldn't fast (given permission by 2:184), or those who preferred not to fast even tough they are Muslim, or those who don't believe in fasting in Ramadan, hence they are not fasting. Assume that one of the above people is starving or so sick and needs to eat or drink (surely not alcohol) and couldn't find anywhere else other than this man's restaurant. Isn't it great thawab to feed that person? This is an extreme example but I hope you get the point.
A Muslim can serve all these people by providing food in his/her restaurant. I don't know of a verse or any implication in Quran that prohibits such an action.
EDIT: Having said that, if I was a restaurant owner, I would re-arrange my restaurant (if necessary and if possible) so that the food I cook/serve and the people who eat in my restaurant will not be visible to the public, among which may be people who are fasting, because they may have additional difficulty by seeing the food and people eating.