11 papers
Obstructions to the full Hao-Ng isomorphism
Adam Dor-On, Ian Thompson
We show that the Hao-Ng isomorphism for full crossed products fails to hold. More precisely, for a non-degenerate -correspondence over a -algebra and a…
Local presentability and monadicity of forgetful functors for operator algebraic categories
Alexandru Chirvasitu, Ian Thompson
In recent work of Lindenhovius and Zamdzhiev, it was established that the category of complete operator spaces, with completely contractive linear maps as morphisms, is locally cou…
Couniversality for C*-algebras of residually finite-dimensional operator algebras
Adam Humeniuk, Christopher Ramsey, Ian Thompson
The C*-envelope of a non self-adjoint operator algebra is known to encode many properties of the underlying subalgebra. However, the C*-envelope does not always encode the residual…
The Hao-Ng isomorphism theorem for reduced crossed products
Adam Dor-On, Ian Thompson
We prove the Hao-Ng isomorphism for reduced crossed products by locally compact Hausdorff groups. More precisely, for a non-degenerate -correspondence and a gener…
Rigidity of operator systems: tight extensions and noncommutative measurable structures
Raphaël Clouâtre, Ian Thompson
Let be a unital -algebra generated by some separable operator system . More than a decade ago, Arveson conjectured that is hyperrigid in if all irreducible repr…
An approximate unique extension property for completely positive maps
Ian Thompson
We study the closure of the unitary orbit of a given point in the non-commutative Choquet boundary of a unital operator space with respect to the topology of pointwise norm converg…
Jensen polynomials associated with Wright's circle method: Hyperbolicity and Turán inequalities
Jashan Bal, Fern Haraldson, Joshua Males +1
We study the Fourier coefficients of functions satisfying a certain version of Wright's circle method with finitely many major arcs. We show that the Jensen polynomials associated…
Minimal boundaries for operator algebras
Raphaël Clouâtre, Ian Thompson
We study boundaries for unital operator algebras. These are sets of irreducible -representations that completely capture the spatial norm attainment for a given subalgebra. Clas…
The number of locally invariant orderings of a group
Idrissa Ba, Adam Clay, Ian Thompson
We show that if a nontrivial group admits a locally invariant ordering, then it admits uncountably many locally invariant orderings. For the case of a left-orderable group, we prov…
Maximal C^*-covers and residual finite-dimensionality
Ian Thompson
We study residually finite-dimensional (or RFD) operator algebras which may not be self-adjoint. An operator algebra may be RFD while simultaneously possessing completely isometric…
Finite-dimensionality in the non-commutative Choquet boundary: peaking phenomena and -liminality
Raphaël Clouâtre, Ian Thompson
We explore the finite-dimensional part of the non-commutative Choquet boundary of an operator algebra. In other words, we seek finite-dimensional boundary representations. Such rep…