Rate My Professor Sonja Mouton

Sonja Mouton is a Professor in the Mathematics Division of the Department of Mathematical Sciences at Stellenbosch University. She is a prominent member of the Functional Analysis research group, which investigates normed, Banach, and Hilbert spaces, operators on these spaces, and generalizations such as Banach algebras. Her work centers on spectral theory of operators and Banach algebras, essential for solving differential and integral equations and extending matrix eigenvalue theory. Key research themes include strongly continuous semigroups of operators, particularly multiplication operators on vector-valued function spaces and stability concepts, as well as operator-theoretic aspects of ergodic theory. Mouton's contributions encompass spectrum-preserving mappings, finite rank elements, Fredholm theory, Drazin inversion, and spectral theory in ordered Banach algebras. Specific advancements involve applications of the scarcity theorem, domination by ergodic elements, upper Browder spectrum properties, links between boundary and exponential spectra, r-Fredholm theory, eigenvalues and stability of multiplication operators, lower Weyl and Lozanovsky spectra, and spectral mapping theorems. She collaborates with group members Dr. Ronalda Benjamin and Dr. Retha Heymann, as well as international partners in South Africa, Germany, Ireland, the Netherlands, the UK, and Zambia.

Mouton completed her PhD at Stellenbosch University in December 2012 with the dissertation 'Spectral Theory in Commutatively Ordered Banach Algebras,' generalizing results from ordered Banach algebras to commutatively ordered settings. Promoted to Associate Professor prior to her doctoral graduation, she advanced to full Professor and delivered her inaugural lecture on 3 October 2023, highlighting the beauty and elegance of spectral theory in ordered Banach algebras. Her publication record features over 30 papers, including recent ones such as 'Ergodic domination in ordered Banach algebras with disjunctive order unit' (2026, with Dimbinaina Ralaivaosaona), 'More on restricted boundaries' (2025, with Robin Harte), 'The restricted connected hull: filling the hole' (2023), 'Generalized Spectral Perturbation and the Boundary Spectrum' (2021), and two 2024 publications—one in Quaestiones Mathematicae with PhD student Dimbinaina Ralaivaosaona. She presented a plenary talk on Fredholm theory and r-Fredholm theory in ordered Banach algebras at Positivity X in Pretoria (2019) and serves on the South African National Committee for the International Mathematics Union (SANCIMU). Mouton supervises PhD students on topics like generalized ergodic domination.