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arXiv · 1311.5265

Atomic representations of Cuntz algebras

Dorin Ervin Dutkay·John Haussermann·Palle E. T. Jorgensen
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Abstract

To a representation of $\O_N$ (the Cuntz algebra with $N$ 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 $S_i^*$. 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.

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Dorin Ervin Dutkay, John Haussermann, Palle E. T. Jorgensen. 2013-11-20. Atomic representations of Cuntz algebras. https://arxiv.org/abs/1311.5265

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