Date of Award
Program or Major
Doctor of Philosophy
In 1994 D. Hadwin introduced the notion of a reflexivity triple (X,Y,E) and defined a very general notion of reflexivity, called
E-reflexivity, for a linear subspace of the vector space X. Hadwin's general version included many special versions (algebraic reflexivity,
topological reflexivity, approximate reflexivity, hyperreflexivity) that had been studied for linear spaces of linear transformations on a vector space or Hilbert space. In this thesis we extend Hadwin's notion and define and study
the abstract notion of reflexivity for an absolutely convex subset of X. We have extended many of Hadwin's results and obtained some new ones. We have also extended Hadwin's generalized notion of direct integrals from measurable families of linear spaces to absolutely convex sets.
Lak, Mahtab, "General Reflexivity For Absolutely Convex Sets" (2019). Doctoral Dissertations. 2454.