Spectral trajectories, duality and inductive-projective limits of Hilbert spaces

An explicit representation of the topological dual of the inductive limit space H4 generated by a colllection R of s.a. operators, has been found in the form of a space of spectral trajectories. i.e .. vector-valued measures with the orthogonal scattering property. This paper is a continuation of (5) completing the previous theory. Illustrations of this type of spaces can be derived from distribution theory and Gel'fand triples theory. At the end of Section 5 we give a short summary on these matters