This paper examines several questions regarding Banach spaces, completeness and compactness of Banach spaces, dual spaces and weak and weak* topologies. Examples of completeness and isometries are given using the cā and šį“° spaces. The Hahn-Banach extension theorem is presented, along with some applications. General theory about finite and infinite dimensional normed linear spaces is the bulk of the second chapter. A proof of the uniform boundedness principle is also given. Chapter three talks in detail about dual spaces and weak and weak* topologies. An embedding proof and proofs involving weak and weak compactness are also given. The Cauchy-Bunyakowski-Schwarz inequality and Alaoglu's theorem are also proven.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc500475 |
| Date | 08 1900 |
| Creators | Kirk, Andrew F. (Andrew Fitzgerald) |
| 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 | iii, 68 leaves, Text |
| Rights | Public, Kirk, Andrew F. (Andrew Fitzgerald), Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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