We find an analytic formulation of the notion of Hopf image, in terms of the associated idempotent state. More precisely, if π:A → Mₙ(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 Cesàro limit of the linear functional φ = tr ∘ π. We then discuss some consequences of this result, notably to inner linearity questions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba60-2-3,
author = {Teodor Banica and Uwe Franz and Adam Skalski},
title = {Idempotent States and the Inner Linearity Property},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {60},
year = {2012},
pages = {123-132},
zbl = {1250.28009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba60-2-3}
}
Teodor Banica; Uwe Franz; Adam Skalski. Idempotent States and the Inner Linearity Property. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 60 (2012) pp. 123-132. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba60-2-3/