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.
Prof. 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 Kelvin Muzundu, Retha Heymann and Ronalda Benjamin. The following are some recent publications which demonstrate Prof. Mouton's interest in spectral theory in Banach algebras and ordered Banach algebras:
- S. Mouton: A condition for spectral continuity of positive elements. Proceedings of the American Mathematical Society 137(5), 2009, 1777 – 1782.
- H. du T. Mouton, S. Mouton and H. Raubenheimer: Ruston elements and Fredholm theory relative to arbitrary homomorphisms. Quaestiones Mathematicae 34, 2011, 341 – 359.
- S. Mouton and K. Muzundu: Commutatively ordered Banach algebras. Quaestiones Mathematicae 36(4), 2013, 559 – 587.
- S. Mouton and K. Muzundu: Domination by ergodic elements in ordered Banach algebras. Positivity 18, 2014, 119 – 130.
- S. Mouton: Applications of the scarcity theorem in ordered Banach algebras. Studia Mathematica 225, 2014, 219-234.
For more information please contact Prof S. Mouton.