English

Pure states on O_d

funct-an 2016-08-15 v1 Operator Algebras

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.

Keywords

Cite

@article{arxiv.funct-an/9711004,
  title  = {Pure states on O_d},
  author = {Ola Bratteli and Palle E. T. Jorgensen and Akitaka Kishimoto and Reinhard F. Werner},
  journal= {arXiv preprint arXiv:funct-an/9711004},
  year   = {2016}
}

Comments

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

R2 v1 2026-07-22T12:30:52.613Z