  Herein is presented a research with regard to the calculation of quantum mean
values, for a composite A+B, by using different formulas to expressions in
Boltzmann-Gibbs-Shannon's statistics. It is analyzed why matrix formulas E_A y
E_B, in Hilbert subspaces, produce identical results to full Hilbert space
formulas. In accord to former investigations, those matrices are the adequated
density matrices, inside third version of nonextensive statistical mechanics.
Those investigations were obtained by calculating the thermodynamical
parameters of magnetization and internal energy. This publication demonstrates
that it is not necessary postulate the mean values formulas in Hilbert
subspaces, but they can be stem from full Hilbert space, taking into
consideration the statistical independence concept.
