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Mathematics Research Report MRR95-040
Endomorphisms Of B(H) II: Finitely Correlated States On
On
O. Bratteli and P.E.T. Jorgensen
Abstract:
We identify sets of conjugacy classes of ergodic endomorphisms of
B(H)
where H is a fixed separable Hilbert space. They correspond to
certain
equivalence classes of pure states on the Cuntz algebras
On where
n is the
Powers index. These states, called finitely correlated states, and strongly
asymptotically shift invariant states, are defined and characterized. The
subsets of
these states defining shifts will in general be identified in [BJW], but here an
interesting cross section for the conjugacy classes of shifts called
diagonalizable
shifts is introduced and studied.
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