On pairs of operators satisfying semilinear relations
We study the relationship between pairs of self-adjoint operators satisfying semilinear relations and representations of nonoriented graphs. The condition of orthoscalarity for representation of a graph is rewritten in terms of the operators. We give examples of semilinear relations for which the corresponding graph is a Dynkin or extended Dynkin graph, and therefore, the corresponding *-representation problem is tame.
Joint work with Pavel Omelchenko.