The constructive theory of operator algebras.
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
The present work is a first step towards a systematic constructive development of the theory of operator algebras over a Hilbert space H. Among the topics investigated in the thesis are locally convex topologies, the extension and characterisation of ultraweakly continuous linear functionals on ß (H), and conditions that ensure the (constructive) existence of the adjoint of a bounded linear operator on H. We also study the relationship between a linear subset of ß (H) and the dual of its predual, and the comparison of projections in a von Neumann algebra. The two appendices to the thesis deal, respectively, with weak continuity properties and the locatedness of the range of an operator.