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arXiv · 1610.01818

An invariant of states on Cuntz algebras

Katsunori Kawamura
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Abstract

For an arbitrary state $\omega$ on a Cuntz algebra, we define a number $1\leq \kappa(\omega)\leq \infty$ such that if the GNS representations of $\omega$ and $\omega'$ are unitarily equivalent, then $\kappa(\omega)=\kappa(\omega')$. By using $\kappa$, we define minimal states and it is shown that the classification problem of states is reduced to that of minimal states. By using results of Dutkay, Haussermann, and Jorgensen, we give a sufficient condition of the minimality of a state. Properties of $\kappa$ and examples are shown. As an application, a new invariant of a certain class of endomorphisms of ${\cal B}({\cal H})$ is given.

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Katsunori Kawamura. 2016-10-06. An invariant of states on Cuntz algebras. https://arxiv.org/abs/1610.01818

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