Research objectives and content
The project aims at creating new insight into the structure of the Banach algebra B(X) of all operators in a Banach space X and certain closed ideals in B(X). The focus is in particular on the interplay between the specific properties of the Banach space X and the structure of these Banach algebras. The research concentrates on two themes: 1. Let A be one of the above-mentioned Banach algebras. When is A amenable? If A is not amenable, then I wish to investigate whether A satisfies certain weaker conditions. 2. When does a certain short exact sequence split? If it splits, can the splitting homomorphism always be chosen to be continuous? The main tool in these studies is K-theory. I plan to compute the K-groups of Banach algebras of the above-mentioned kind, and I wish to determine which pairs of abelian groups that arise as (Ko(B(X)),K1(B(X))) for some Banach space X.
Training content (objective, benefit and expected impact)
I will be trained as a researcher in pure mathematics through my cooperation with experienced mathematicians (notably H.G. Dales and the team in functional analysis) at the University of Leeds and its neighbouring universities and through my participation in seminars on functional analysis and K-theory.
Links with industry / industrial relevance (22)