Abstract
This paper contains a thorough investigation of topological, geometrical, and structural properties of Fréchet 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 Fréchet spaces and their strong duals. In particular, these results are applicable for representing the topologies of the space of test functions and the space of generalized functions.
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