Complete sets of diagonal operators, i.e. operators commuting with the hamiltonian of a physical system, are constructed. In terms of these sets all diagonal operators can be written as a series, the uniform convergence of which is studied for infinitely large systems. This uniform convergence is introduced as a possible criterion for ergodicity.
Caspers, W. J., van de Braak, H. P., Verbeek, P. W., & Verstelle, J. C. (1971). Complete sets of diagonal operators in quantum-statistical mechanics. Physica, 53(2), 210-224. https://doi.org/10.1016/0031-8914(71)90071-1