NORMAL SYMMETRIC DYNAMICAL SYSTEMS.

A form of the state space isomorphism theorem is established for linear differentiable dynamical systems in a Hilbert space, and some application of these results is made. The methods used are based on spectral representations and suggest a close connection between the state space isomorphism theorem and certain classical representation theorems in analysis. A class of counterexamples is also given which illuminate the difficulties in extending the finite-dimensional theory thus justifying, in part, the stronger hypothesis used here.