The purpose of this paper is to explore certain properties of Banach spaces. The first chapter begins with basic definitions, includes examples of Banach spaces, and concludes with some properties of continuous linear functionals. In the second chapter, dimension is discussed; then one version of the Hahn-Banach Theorem is presented. The third chapter focuses on dual spaces and includes an example using co, RI, and e'. The role of locally convex spaces is also explored in this chapter. In the fourth chapter, several more theorems concerning dual spaces and related topologies are presented. The final chapter focuses on reflexive spaces. In the main theorem, the relation between compactness and reflexivity is examined. The paper concludes with an example of a non-reflexive space.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc500848 |
| Date | 08 1900 |
| Creators | Dahler, Cheryl L. (Cheryl Lewis) |
| Contributors | Lewis, Paul Weldon, Hagan, Melvin R. |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iv, 62 leaves : ill., Text |
| Rights | Public, Copyright, Dahler, Cheryl L. (Cheryl Lewis), Copyright is held by the author, unless otherwise noted. All rights reserved. |
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