Dirac formulation of quantum mechanics: Recent and new results

We make a summary of recent and new results concerning the mathematics of the Diracformulation of quantum mechanics. Two problems are discussed in here. The former is the construction for tight riggings for every quantum observable with continuous spectrum. The solution is given in terms of minimal riggings, minimal with respect to some ordering. We also give a formula that gives the integral kernel for the change of representation, under given conditions.