In this paper the weak completeness of certain sequence spaces is examined. In particular, we show that each of the sequence spaces c0 and 9, 1 < p < c, is a Banach space. A Riesz representation for the dual space of each of these sequence spaces is given. A Riesz representation theorem for Hilbert space is also proven. In the third chapter we conclude that any reflexive space is weakly (sequentially) complete. We give 01 as an example of a non-reflexive space that is weakly complete. Two examples, c0 and YJ, are given of spaces that fail to be weakly complete.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc504338 |
| Date | 08 1900 |
| Creators | Leavelle, Tommy L. (Tommy Lee) |
| Contributors | Lewis, Paul Weldon, Bilyeu, Russell Gene |
| Publisher | North Texas State University |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iii, 50 leaves, Text |
| Rights | Public, Leavelle, Tommy L. (Tommy Lee), Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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