Date of Award

Spring 2019

Project Type

Dissertation

Program or Major

Mathematics

Degree Name

Doctor of Philosophy

First Advisor

Don Hadwin

Second Advisor

Eric Nordgren

Third Advisor

Junhao Shen

Abstract

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.

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