  We investigate the properties of the simultaneous projection method as
applied to countably infinitely many closed and linear subspaces of a real
Hilbert space. We establish the optimal error bound for linear convergence of
this method, which we express in terms of the cosine of the Friedrichs angle
computed in an infinite product space. In addition, we provide estimates and
alternative expressions for the above-mentioned number. Furthermore, we relate
this number to the dichotomy theorem and to super-polynomially fast
convergence. We also discuss polynomial convergence of the simultaneous
projection method which takes place for particularly chosen starting points.
