Pure states on O_d

Details Pure states on O_d Pure states on O_d

1997-11-21

arxiv.org/abs/funct-an/9711004v1

J. Operator Theory 43 (2000), 97--143

Mathematics

Operator Algebras

42 pages, 0 figures, AMS-LaTeX v1.2b

Scientific paper

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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