English

Atomic representations of Cuntz algebras

Operator Algebras 2013-11-22 v1 Functional Analysis

Abstract

To a representation of \ON\O_N (the Cuntz algebra with NN generators) we associate a projection valued measure and we study the case when this measure has atoms. The main technical tool are the spaces invariant for all the operators SiS_i^*. We classify the purely atomic representations and find when such representations are permutative. Applications include: wavelet representations, representations generated by finitely correlated states, representation associated to Hadamard triples (or fractal spectral measures) and representations associated to generalized Walsh bases.

Keywords

Cite

@article{arxiv.1311.5265,
  title  = {Atomic representations of Cuntz algebras},
  author = {Dorin Ervin Dutkay and John Haussermann and Palle E. T. Jorgensen},
  journal= {arXiv preprint arXiv:1311.5265},
  year   = {2013}
}