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The area of research within Pure Mathematics Dr Mathieu has been involved in over the last number of years can be most adequately described as Noncommutative Functional Analysis.

Traditional Functional Analysis, as it was formed by Stefan Banach early in the 20th century on the basis of the work of many others, seeks to understand Banach spaces and operators between them. Noncommutative Functional Analysis grew out of the theory of C* -algebras, which are algebras of bounded linear operators on Hilbert space.

The new structure arises by enriching a Banach space with a 'noncommutative' structure allowing an embedding into a space of operators on Hilbert space. Being a subspace of an algebra whose multiplication is in general noncommutative, many new features appear for an operator space which are invisible or non-existent at the Banach space level.

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  • What is non–commutative Functional Analysis about? 
    The Irish Scientist Year Book, Oldbury Publ., Dublin 2004


Faculty of Engineering and Physical Sciences

School of Mathematics and Pyhsics

Research students

PhD title: Interplay between noncommutative topology and operators on C*- algebras

Name: Jürgen Schweizer,
Years of Study: February 1997

PhD title: Commutativity preserving mappings on C*- algebras

Name: Ralf Banning
Years of Study: April 1998


Phd Title: Spectrally bounded operators on Banach algebras

Name: Gerhard Schick
Years of Study: December 2001

Research at Queen's

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