School of Mathematics and Statistics - Functional Analysis Research Group

The use of techniques of functional analysis to study families of operators leads naturally to the concept of an operator algebra. This area of mathematics is at the centre of a host of current applications: quantum mechanics, statistical mechanics, imaging techniques, to name only three.

Interests of the group range from single operator theory in Banach spaces through semigroup theory to von Neumann and C*-algebras. There is significant interaction with the harmonic analysis group.

Group Members

S. Ajiev(Research Associate),
T. Bates (Lecturer),
A.Dooley (Professor),
I. Doust (Associate Professor),

G. Gaudry (Emeritus Professor),

V. Golodets (Visiting Fellow),

H. Grundling (Senior Lecturer),

A. an Huef (Senior Lecturer),

B. Jefferies (Senior Lecturer),

C. Sutherland (Professor)

Research Students

Collaborators

Robert Archbold, University of Aberdeen, UK
Lisa Orloff Clark, Susquehanna University, USA
Soeren Eilers, University of Copenhagen, Denmark
T.A. Gillespie, University of Edinburgh, UK
Thierry Giordano, University of Ottawa, Canada
Steven Kaliszewski, Arizona State University, USA
John Phillips, University of Victoria, Canada
Iain Raeburn, University of Newcastle, Australia
Dana Williams, Dartmouth College, USA

Research Interests

Teresa Bates is interested in the C*-algebras associated to directed and labelled directed graphs. She is currently studying the connections between graph algebras and associated subshifts arising in topological dynamics and ergodic theory.

Sergey Bezuglyi is a senior researcher from the Ukrainian Academy of Sciences in Kharkov. He has spent a number of periods of several months as a research associate, working with Tony Dooley on aspects of ergodic theory.

Michael Cowling's interests in this area complement his work in harmonic analysis and extend from the study of semigroups of operators on to recent joint work with Haagerup which resulted in a new classification of type II von Neumann algebras.

Tony Dooley has interests in non-singular ergodic theory. He has studied G-measures and Markov measures and their applications to non-singular systems. Recently he has been working on the classification of systems of type III₀.

Ian Doust works in single operator theory, specifically the spectral theory of linear operators acting in Banach spaces. His work on the interaction between the geometry of Banach spaces and functional calculi has lead naturally to integral representations of operators.

Garth Gaudry is interested in functional calculi for differential operators and other classical operators. He also has interests in Harmonic Analysis. Some of his recent publications may be viewed here.

Valentin Golodets retired from the Institute of Low Temperature Physics, in Kharkov. He is a visiting fellow in the school who is working with Tony Dooley on ergodic theory.

Astrid an Huef studies the operator algebras associated to transformation groups and C*-dynamical systems. She is currently invesitigating proper actions and the amenability of systems. For more information, including some of Astrid's recent publications, click here.

Brian Jefferies has interests in the theory of vector measures with applications to functional integration and Feynman path integrals. He is currently working on functional calculi for non-commuting systems of operators. His monograph Spectral Properties of Noncommuting Operators, Lecture Notes in Mathematics 1843 was published by Springer in 2004.

Colin Sutherland's wide interests have their initial impetus in von Neumann algebras but have significant intersection with the harmonic analysis of non-Type I groups and the study of cocycles in ergodic theory. He has worked in the theory of groupoids an extension of the notion of group action. He is currently using ideas from graph theory to study approximately finite dimensional von Neumann algebras.