I've been searching google and scholar google, but i only have come upon orderings and Hermitian forms on *-fields.

Has real algebraic geometry been carried over to *-rings? *-rings are rings with an involution. For example are there Positivstellensätze and characterizations of sums of squares by total positivity etc.

If anyone has references, it would be of great help. Books, papers or online resources are all great. thanks in advance.