On some topological and geometrical properties of Frechet–Hilbert spaces

This paper contains a thorough investigation of topological, geometrical, and structural properties of Frechet spaces representable as a strict projective limit of a sequence of Hilbert spaces, and also of their strong duals, which are representable as a strict inductive limit of a sequence of Hilbert spaces. With the help of families of these spaces, representations are given for the topologies of strict inductive limits of nuclear Frechet spaces and their strong duals. In particular, these results are applicable for representing the topologies of the space $\mathscr D$ of test functions and the space $\mathscr D'$ of generalized functions.