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arXiv · 1112.5018

Idempotent states and the inner linearity property

Teodor Banica·Uwe Franz·Adam Skalski
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Abstract

We find an analytic formulation of the notion of Hopf image, in terms of the associated idempotent state. More precisely, if $\pi:A\to M_n(\mathbb C)$ is a finite dimensional representation of a Hopf $C^*$-algebra, we prove that the idempotent state associated to its Hopf image $A'$ must be the convolution Ces\`aro limit of the linear functional $\phi=tr\circ\pi$. We discuss then some consequences of this result, notably to inner linearity questions.

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Teodor Banica, Uwe Franz, Adam Skalski. 2011-12-21. Idempotent states and the inner linearity property. https://doi.org/10.4064/ba60-2-3

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