The d-dimensional 2-spin facilitated kinetic Ising model is studied analytically starting from usual master equations and their transformation into a Fock-space representation. The evolution of relevant operators is rewritten in terms of a projection formalism. The obtained frequency matrices and memory terms are analyzed. Especially, the structure of the memory terms is approached by using the well-known factorization approximation as the standard decomposition technique of N-point correlation functions. The temperature dependence of the relaxation times related to the 2-spin facilitated kinetic Ising model shows a non-Arrhenius behavior. Furthermore, a characteristic stretched decay of the correlation function is obtained.