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…
The ideal separation property for reduced group -algebras
Are Austad, Hannes Thiel
We say that an inclusion of an algebra into a -algebra has the ideal separation property if closed ideals in can be recovered by their intersection with . Such…
Quantum metrics on crossed products with groups of polynomial growth
Are Austad, Jens Kaad, David Kyed
We show how to equip the crossed product between a group of polynomial growth and a compact quantum metric space with a compact quantum metric space structure. When the quantum met…
Polynomial growth and property for étale groupoids with applications to -theory
Are Austad, Eduard Ortega, Mathias Palmstrøm
We investigate property for étale groupoids and apply it to -theory of reduced groupoid -operator algebras. In particular, under the assumption of polynomial growth,…
Detecting ideals in reduced crossed product C*-algebras of topological dynamical systems
Are Austad, Sven Raum
We introduce the -ideal intersection property for crossed product C*-algebras. It is implied by C*-simplicity as well as C*-uniqueness. We show that topological dynamical s…
Groupoids and Hermitian Banach *-algebras
Are Austad, Eduard Ortega
We study when the twisted groupoid Banach -algebra is Hermitian. In particular, we prove that Hermitian groupoids satisfy the weak containment property. Fur…
-uniqueness Results for Groupoids
Are Austad, Eduard Ortega
For a second-countable locally compact Hausdorff étale groupoid with a continuous -cocycle we find conditions that guarantee that has…
Spectral invariance of -representations of twisted convolution algebras with applications in Gabor analysis
Are Austad
We show spectral invariance for faithful -representations for a class of twisted convolution algebras. More precisely, if is a locally compact group with a continuous -co…
Gabor Duality Theory for Morita Equivalent -algebras
Are Austad, Mads S. Jakobsen, Franz Luef
The duality principle for Gabor frames is one of the pillars of Gabor analysis. We establish a far-reaching generalization to Morita equivalent -algebras where the equivalence…
Heisenberg modules as function spaces
Are Austad, Ulrik Enstad
Let be a closed, cocompact subgroup of , where is a second countable, locally compact abelian group. Using localization of Hilbert -modules, we s…
Modulation Spaces as a Smooth Structure in Noncommutative Geometry
Are Austad, Franz Luef
We demonstrate that a class of modulation spaces are examples of a smooth structure on the noncommutative 2-torus in the sense of recent developments in KK-theory. In addition, we…