Analysis: Research

Research Interests

H. Garth Dales (Retired)	I work in the general theory of Banach algebras. I am interested in their algebraic structure, and in the automatic continuity of homomorphisms between Banach algebras. The algebraic structure involves questions on the decomposition of non-semisimple Banach algebras into semisimple and radical parts. It will be seen that work in this area is based in functional analysis, but has an algebraic flavour.
Matt Daws	I am interested in many aspects of what algebra meets analysis: principally Banach and operator algebras arising in abstract harmonic analysis, and related areas. I have recently become interested in "topological" quantum groups: using the framework of operator algebras to study quantum groups. Typical problems I study will originate as a (Banach) algebraic question, but will often need tools from operator algebras for their solution.
Vladimir Kisil	Operator and C*-algebras with symmetries, particularly algebra of convolutions and pseudodifferential operators on Lie groups and homogeneous spaces; Functional calculus of operators and associated notions of (joint) spectrum of operators; Hilbert spaces of analytic functions with reproducing kernels arising from group representations in complex and Clifford analysis; Applications of coherent states, wavelet transform and group representations in quantum mechanics, combinatorics, etc.
Jonathan Partington	My research interests centre on operator theory and Banach spaces of analytic functions. These include very abstract questions about invariant subspaces, where tools from complex analysis have been found useful, and also the study of particular types of operator, such as Hankel, Toeplitz and composition operators. I am very interested in applications of operator theory, which include the study of linear semigroup systems, control theory and partial differential equations.
Charles Read	Operator theory, invariant subspaces, hypercyclicity. Banach algebras, ideals, amenability.
Nicholas Young (Research professor)	Mathematical analysis, particularly operators on Hilbert space; complex analysis; H infinity control. Recent work, in collaboration with Jim Agler (UC San Diego) and John E. McCarthy (Washington University), is on the extension of some classical theorems of function theory to functions of two variables.

Recent and forthcoming meetings

Banach algebra and operator space techniques in topological group theory, May/June 2010.
Graduate student mini-meeting on operator theory and spaces of analytic functions, December 17th-18th 2008.
Banach algebras and harmonic analysis, April 22nd-23rd 2008
NBFAS, November 2nd-3rd 2007
Banach algebras mini-meeting, May 15th-16th 2007
Meeting to mark the retirement of Prof. E.C. Lance, September 21st-23rd 2006
London Mathematical Society regional meeting and workshop, July 3rd-7th 2006
Meeting on Banach algebras and cohomology, April 22nd-23rd 2005
NBFAS, March 4th-5th 2005
International workshop on invariant subspaces, July 3rd-5th 2003

Recent Books

Modern Approaches to the Invariant-Subspace Problem by J.R. Partington et al. (C.U.P.)
Introduction to Banach Spaces and Algebras, edited by H.G. Dales (O.U.P.)
Banach Algebras and Automatic Continuity, by H.G. Dales (O.U.P.)
Introduction to Banach Algebras, Operators, and Harmonic Analysis, by H.G. Dales et al. (C.U.P.)
Linear Operators and Linear Systems, by J.R. Partington (C.U.P.)
Harmonic Analysis and Rational Approximation, ed. J.R. Partington et al. (Springer)

Recent visitors

We have many visitors to the Analysis group, staying from a week to a number of months, and making use of the Research Visitors' Centre.

Ondrej Hutnik (September 2011).
Sandra Pott (Most recently, September 2011).
Birgit Jacob (Most recently, September 2011).
Juliette Leblond (June 2011).
Dr. Debapriya Biswas (June 2011).
Luis Sanchez-Lajusticia (January-March 2011).
Tony Lau (Most recently, December 2010).
Semyon Yakubovich (August 2010).
Many visitors attended the "working semester" in Banach algebra and operator space techniques in topological group theory (May/June 2010).
Jan Cnops (March 2010).
Hung Le Pham (Spring 2010).
Sergei Rogosin (December 2009).
Pedro J. Miana (Winter 2009).

Recent PhD theses

Dr S. Elliott -- Composition Operators and Aleksandrov-Clark Measures (2010)
Dr P. Ramsden -- Homological properties of semigroup algebras (2009)
Dr P. Lawson -- Ideals in Banach algebras and notions of amenability (2008)
Dr M. de la Rosa -- Hypercyclic operators: and related topics (2008)
Dr S. Barclay -- Banach spaces of analytic vector-valued functions (2007)