Herein is presented a research concerning 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 with matrices E A and E B, in Hilbert subspaces, produce identical results to full Hilbert space formulas. In accord to former investigations, those matrices are the true density matrices, inside third version of nonextensive statistical mechanics. Those investigations were obtained by calculating the thermodynamical parameters of magnetization and internal energy for magnetic materials. This publication shows that it is not necessary postulate the mean value formulas in Hilbert subspaces, but they can be formally derived from full Hilbert space, taking into consideration the very statistical independence concept. © Electronic Journal of Theoretical Physics. All rights reserved.