ENDOMORPHISMS OF B(H) .2. FINELY CORRELATED STATES ON O-N

We identify sets of conjugacy classes of ergodic endomorphisms of B(H) where H is a fixed separable Hilbert space. They correspond to certai n equivalence classes of pure states on the Cuntz algebras O-n where n is the Powers index. These states, called finitely correlated states, and strongly asymptotically shift invariant states, are defined and c haracterized. The subsets of these stares defining shifts will in gene ral be identified in a later work, but here an interesting cross secti on for the conjugacy classes of shifts called diagonalizable shifts is introduced and studied. (C) 1997 Academic Press.