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Pure states on O_d

Ola Bratteli·Palle E. T. Jorgensen·Akitaka Kishimoto·Reinhard F. Werner
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Abstract

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

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BibTeXRIS

Ola Bratteli, Palle E. T. Jorgensen, Akitaka Kishimoto, Reinhard F. Werner. 1997-11-21. Pure states on O_d. https://arxiv.org/abs/funct-an/9711004

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