Degrees: M.Sc., Ph.D. (Cape Town)
Email: nrcr@maths.uct.ac.za
Teaching and research interests:
Locally convex spaces: This is a subject which lies near the heart of modern Functional Analysis: it has connections to a wide variety of other fields, such as Measure Theory, Operator Theory, Linear Algebra and Topology. The basic problem is to extend results which describe the geometry of Banach spaces to more general classes of topological vector spaces. This entails a close study of the topologies which can be defined on these spaces; it becomes necessary to explore such topics as the Radon-Nikodým Property, infinite-dimensional holomorphy, operator ideals and descriptive set theory.Computer Algebra Systems: Applications of packages such as Maple and Mathematica to teaching and research. Dynamical systems and chaos: Fractals, chaos and iterated function systems.
Representative publications:
- The metrisability of precompact sets, Bull. Austral. Math. Soc. 43 (1991), 131-135.
- Dentability in locally convex spaces, Quaestiones Mathematicae 14 (1991), 105-110.
- Extending Edgar's ordering to locally convex spaces, Glasgow Math. J. 34 (1992), 175-188.
- Asplund operators and holomorphic maps, Manuscripta Math. 75 (1992) 25-34.