Positive Sets, Conservative Sets and Dissipative Sets

We look for a simple general framework which would encompass the notion of symmetric self-dual spaces introduced by S. Simons and the notion of self-paired product space proposed recently by the author ["Monotonicities and dualities", in: Generalized Convexity and Related Topics, I. V. Konnor, D. T. Luc and A. M. Rubinov (eds), Lecture Notes in Economics and Math. Systems 583, Springer, Berlin (2007), 300-414]. Such a framework is appropriate for the study of a notion generalizing the concept of monotone operator. The representation of such operators by functions is the main purpose of the study.