We study weak convergence of sequences in Banach spaces. In particular, we compare
the notions of weak and norm convergence. Although these modes of convergence usually
differ, we show that in โยน they coincide. We then show a theorem of Rosenthal's which
states that if {๐โ} is a bounded sequence in a Banach space, then {๐โ} has a subsequence
{๐'โ} satisfying one of the following two mutually exclusive alternatives; (i) {๐'โ} is weakly
Cauchy, or (ii) {๐'โ} is equivalent to the unit vector basis of โยน.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc500521 |
| Date | 12 1900 |
| Creators | Hymel, Arthur J. (Arthur Joseph) |
| Contributors | Bator, Elizabeth M., Bilyeu, Russell Gene, Lewis, Paul Weldon |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iii, 71 leaves, Text |
| Rights | Public, Hymel, Arthur J. (Arthur Joseph), Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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