Details

Autor(en) / Beteiligte

• BERGMANN, WOLFGANG R.
• CONTI, ROBERTO

Titel

Asymptotic invariance, amenability and generalized Cuntz algebras

Ist Teil von

• Ergodic theory and dynamical systems, 2003-10, Vol.23 (5), p.1323-1346, Article S0143385702001748

Ort / Verlag

Cambridge, UK: Cambridge University Press

Erscheinungsjahr

2003

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Given a unitary representation u of the locally compact group G on the Hilbert space H, we investigate the notion of infinite tensor power of u. Then we apply the results to study covariance of the associated canonical action of G on the generalized Cuntz algebra $\mathcal{O}_H$ in the GNS representation of (the gauge-invariant extension of) some pure quasi-free state. We examine in detail the case of a measure-preserving action of G on a measure space X. In this case, covariance is (almost) equivalent to the existence of a G-invariant state on $L^\infty(X)$.