16 citations · 16 across the 13 of their papers we have counts for
16 papers
Compact Quantum Metric Spaces from Weakly Geodesic Length Functions on Hyperbolic Groups
Are Austad
We show that length functions on hyperbolic groups whose induced metrics are hyperbolic and weakly geodesic naturally give rise to compact quantum metric spaces, thus generalizing…
Growth Conditions for Étale Groupoids: Amenability and Comparison
Are Austad, Christian Bönicke
We investigate étale Hausdorff groupoids whose source fibres have controlled growth with respect to a length function. Our first result shows that uniform subexponential growth imp…
Quantum metrics from length functions on étale groupoids
Are Austad
We show how to construct a compact quantum metric space from a proper continuous length function on an étale groupoid with compact unit space, where the unit space additionally has…
Metrics on completely positive maps via noncommutative geometry
Are Austad, Erik Bédos, Jonas Eidesen +2
We study methods of inducing metrics on unital completely positive maps by employing seminorms arising in noncommutative geometry. Our main approach relies on the development of an…
Quantum metrics from length functions on quantum groups
Are Austad, David Kyed
We study the quantum metric structure arising from length functions on quantum groups and show that for coamenable quantum groups of Kac type, the quantum metric information is cap…
K-theory invariance of -operator algebras associated with étale groupoids of strong subexponential growth
Are Austad, Eduard Ortega, Mathias Palmstrøm
We introduce the notion of (strong) subexponential growth for étale groupoids and study its basic properties. In particular, we show that the K-groups of the associated groupoid $L…