I am interested in aspects of abstract algebraic functional analysis, mainly Banach and operator algebras and links to abstract harmonic analysis, with some interest in Banach spaces. I am happy to supervise research students: some possible projects are listed on the Analysis website pages. Recent work with coauthors has:
- Looked at what a closed subgroup of a locally compact quantum group might be.
- Show how completely positive multipliers of operator algebraic quantum groups always arise from unitary corepresentations-- this can be seen as a non-commutative analogy of the study of positive definite functions on groups.
- Studied completely bounded but not *-preserving representations (equivalently, non-unitary corpresentations) of locally compact quantum groups.
- Constructed exotic preduals of the Banach space $\ell^1(\mathbb Z)$ which make the bilateral shift weak-star continuous, as well as initiating the classification of such preduals.
- Studied the abstract theory of multipliers of dual Banach algebras, and applied this to study algebras in abstract quantum harmonic analysis.