Examples of subhomogeneous Banach and operator algebras

Lead Research Organisation: Lancaster University


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509504/1 30/09/2016 29/09/2021
1943819 Studentship EP/N509504/1 30/09/2017 29/09/2021
Description Thus far, work was done to expand on results from a recent work of Choi-Farah-Ozawa (2014) by taking the example amenable operator algebra and doing further investigation on its irreducible representations (including that it is 2-subhomogeneous) and went on to show what the Fell topology looked like on its dual space (this topology was defined by Fell in 1965). The Fell topology for the algebra defined by Choi-Farah-Ozawa was shown to "look like" the natural numbers with some "interesting" points at infinity. All the results proven about this have been made ready to become a chapter in the final thesis.

New work has also begun on an offshoot of the problem from the Choi-Farah-Ozawa paper. In the 2014 paper it was shown that there was an example of an amenable operator algebra that was not isomorphic to a C*-algebra. However, the example found was a subalgebra of bounded sequences of 2 x 2 matrices. The question currently is whether all amenable operator subalgebras of convergent sequences of 2 x 2 matrices are isomorphic to a C*-algebra. The belief is yes, and we seek to prove this.
Exploitation Route Methods used in the current problem of proving that all amenable subalgebras of convergent sequences of 2 x 2 matrices expand on ideas used by Gifford (2006) and will hopefully evolve into a kind of inductive argument which can be used in other cases.
Sectors Other