Research

My research interests are in mathematical analysis, mainly in functional analysis and specifically in operator algebras.

My PhD advisor was Professor N. Christopher Phillips.

My research is on operator algebras on `L^p` spaces which "look like `C^{**}`-algebras". Roughly speaking, this consists of developing an analogous theory for such `L^p`-operator algebras that closely relates to the known theory for `C^{**}`-algebras. The interesting part lies in the fact that there is no concept of adjoint operator in a `L^p` -operator algebra and, therefore, the usual tools used to prove results in a `C^{**}`-algebra setting are not always available. This is a relatively new field of study, so not much is known about it. Some of the tools one needs when working on `L^p`-operator algebras are from the classic theory of `C^{**}`-algebras such as `K`-theory, representation theory and crossed products. However, methods from operator spaces and classical Banach space theory are also helpful here.

I am also interested in abstract harmonic analysis. In particular interaction between wavelets and `C^{**}`-algebras and the spectral synthesis problem for the `L^p` group operator algebra of the integers. The toolbox here inculdes topological groups, commutative Banach algebras, `K`-theory, Hilbert `C^{**}`-modules, and frames and bases.

Published Papers

In preparation