Operator algebras and topological groups Archbold works on several aspects of operator algebras and their representation theory, often in collaboration with Somerset and others:
- upper and lower multiplicities for irreducible representations of C*-algebras, of locally compact groups and of their crossed products, with applications to the strength of convergence in orbit spaces associated to transformation groups and nilpotent Lie groups;
- real rank and stable rank for group C*-algebras;
- norms of inner derivations and other elementary operators on C*-algebras;
- ideal structure in multiplier algebras of C*-algebras;
- extensions and limits of pure states and factorial states of C*-algebras;
Wright's interests are in C*-algebras and relations with non-commutative measure theory and the mathematical foundations of quantum mechanics. One of his most recent achievements, in cooperation with K Saito, is the classification of "small" monotone complete C*-algebras.
- Dr Douglas Somerset