Friedrichs' early contributions are discussed in On the Stone-von Neumann Uniqueness Theorem and Its Ramifications by S.J. Summers:
In the early 1950's, K.O. Friedrichs undertook an influential attempt
to reduce the hand-waving typical of quantum field theory up to that
time [1,2]. The result of greatest interest was his construction of
some representations of the canonical commutation relations for
infinitely many degrees of freedom which were not unitarily
equivalent to the Fock representation.
This development is described by Friedrichs on page 3 of [1]:
In Part IV we shall show that a description of the field in terms of
"occupation numbers", though somewhat unwieldy, can nevertheless be
introduced, even if the spectrum of the energy is not discrete. It
will be seen that there are two types of such occupation number
representations; only one of them is equivalent with a particle
representation. Accordingly, there are different non-equivalent
realizations of the basic field operators, and consequently different - non-equivalent kinds of fields, a fact which seems worth noticing.
[1] K.O. Friedrichs, Mathematical Aspects of the Quantum Theory of Fields, 1953.
[2] The 1953 monograph, in four parts, is based on four earlier publications in Commun. Pure Appl. Math.: 4, 161–224 (1951);
5, 1–56 (1952); 5, 349–494 (1952); 6, 1–72 (1953).
So the "late 1940's" from Reed & Simon should more accurately be "early 1950's".
