Pure states on Od
Ola Bratteli, Palle E. T. Jorgensen, Akitaka Kishimoto, Reinhard F. Werner
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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