FINITELY CORRELATED PURE STATES

We study a w*-dense subset of the translation invariant states on an infinite tensor product algebra x Z A, where A is a matrix algebra. These ''finitely correlated states'' are explicitly constructed in terms of a finite dimensional auxiliary algebra B and a completely positive map E: A x B --> B. We show that such a state omega is pure if and only if it is extremal periodic and its entropy density vanishes. In this case the auxiliary objects B and E are uniquely determined by omega, and can be expressed in terms of an isometry between suitable tensor product Hilbert spaces. (C) 1994 Academic Press, Inc.