Pure states on Od
Abstract
We study representations of the Cuntz algebras Od and their associated decompositions. In the case that these representations are irreducible, their restrictions to the gauge-invariant subalgebra UHFd have an interesting cyclic structure. If Si, 1 ≤ i ≤ d, are representatives of the Cuntz relations on a Hilbert space H, special attention is given to the subspaces which are invariant under Si*. The applications include wavelet multiresolutions corresponding to wavelets of compact support (to appear in the later paper BEJ97), and finitely correlated states on one-dimensional quantum spin chains.
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