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We develop a rigorous formalism for the description of the evolution ofobservables in quantum systems of particles. We construct a solution of theinitial-value problem to the quantum dual BBGKY hierarchy of equations as anexpansion over particle clusters whose evolution are governed by thecorresponding-order dual cumulant (dual semi-invariant) of the evolutionoperators of finitely many particles. For initial data from the space ofsequences of bounded operators the existence and uniqueness theorem is proved.

On the Initial-Value Problem to the Quantum Dual BBGKY Hierarchy