Department of Mathematical Sciences

Mathematics

Functional Analysis

Involving the study of normed, Banach and Hilbert spaces, the operators on them and generalizations of these concepts, this key area of mathematics underpins much of the research and applications in areas of analysis such as measure and probability theory, financial mathematics, quantum field theory in theoretical physics, approximation theory and differential and integral equations. Currently, active research includes questions on Banach and Hilbert spaces, linear operators and their spectra, as well as Banach algebras.

Dr Sonja Mouton coordinates Functional Analysis and has successfully attracted graduate students, who are introduced to the broader mathematical research environment through her own local and international involvement in the area. Her recent and current postgraduate students include Martin Weigt, Kelvin Muzundu and Retha Heymann. The following are some recent publications which demonstrate Dr Mouton’s interest in spectral theory in Banach algebras and ordered Banach algebras:

  1. S. Mouton. On spectral continuity of positive elements. Studia Mathematica 174(1), 2006, 75-84.
  2.  S. Mouton. On the boundary spectrum in Banach algebras. Bulletin of the Australian Mathematical Society 74(2), 2006, 239-246.
  3. S. Mouton. A condition for spectral continuity of positive elements.Proceedings of the American Mathematical Society 137(5), 2009, 1777-1782.
  4. S. Mouton: Mapping and continuity properties of the boundary spectrum in Banach algebras. To appear in Illinois Journal of Mathematics.

For more information please contact Dr S. Mouton.