Invariant subspaces of clustering operators

A class of clustering operators is defined which is a generalization of a transfer matrix of a Gibbs lattice field with an exponential decay of correlations. It is proved that for small values of the clustering operator has invariant subspaces which are similar tok-particle subspaces of the Fock space. The restriction of the clustering operator onto these subspaces resembles the operator exp(-H _k, whereH _k is thek- particle Schrödinger Hamiltonian in nonrelativistic quantum mechanics. The spectrum of eachH _k,k1, is contained in the interval (C ₁^k,C ₂^k). These intervals do not intersect with each other.