Locally solid topologies on Riesz spaces (vector lattices) and the interaction between topological and order structures in such spaces.
C*- and Von Neumann-algebras; their interpretation as non-commutative `function spaces', and the order structures of such spaces.
Teaching: Abstract analysis, both at undergraduate level (e.g. real analysis, metric spaces, Hilbert space, integration theory) and at postgraduate level (functional analysis, topology, measure theory).
Mathematics education, in particular:
The presentation of mathematics not in the school syllabus to school pupils in order to stimulate their interest in mathematics,
discovery methods, and other strategies for encouraging student participation in mathematics lectures.
(with J. Swart) On Schwartz operator ideals determined by the order-bounded sets in a Banach lattice, Bull. Inst. Math. Acad. Sinica 11 (1983), 525-548.
(with J. Swart) A general duality result for precompact sets, Indag. Math. (N.S.) 1 (4), 409-416.
Duality results for order precompact sets in locally solid Riesz spaces Indag. Math. (N.S.) 2(1), 19-28.