On the Formulas for Quantum Mean Values for a Composite A+B

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.