Abstract
This major paper is a report on author’s study of some topics on topological vector spaces. We prove a well-known Hahn-Banach theorem and some important consequences, including several separation and extension theorems. We study the weak topology on a topological vector space X and the weak-star topology on the dual space X* of X. We also prove the Banach-Alaoglu theorem. Consequently, we characterize the closed convex hull and the closed linear span for sets in X and X* , identify the dual of a subspace of X with the quotient of its annihilator, and obtain the Goldstine theorem as well as some characterizations of reflexive normed spaces.
Primary Advisor
Zhiguo Hu
Program Reader
Mehdi Monfared
Degree Name
Master of Science
Department
Mathematics and Statistics
Document Type
Major Research Paper
Convocation Year
2018