Idempotent States and the Inner Linearity Property

• Autorzy: Teodor Banica , Uwe Franz , Adam Skalski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 28C10: Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
• 46L65: Quantizations, deformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: 60
• Numer: 2
• Strony: 123-132

Daty

wydano

2012

Twórcy

autor

Teodor Banica

• Department of Mathematics, Cergy-Pontoise University, 95000 Cergy-Pontoise, France

autor

Uwe Franz

• Department of Mathematics, University of Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France

autor

Adam Skalski

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba60-2-3