Atomic representations of Cuntz algebras
Operator Algebras
2013-11-22 v1 Functional Analysis
Abstract
To a representation of (the Cuntz algebra with 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 . 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}
}