In this thesis, we study two problems. The first one is the renorming problem in
Banach lattices. We state the problem and give some known results related to it.
Then we pass to construct a positive doubly power bounded operator with a nonpositive
inverse on an infinite dimensional AL-space which generalizes the result of
[10].
The second problem is related to the mean ergodicity of positive operators on KBspaces.
We prove that any positive power bounded operator T in a KB-space E
which satisfies
lim
n!1
dist1
n
n& / #8722 / 1 Xk=0
Tkx, [& / #8722 / g, g] + BE= 0 (8x 2 E, kxk 1), ()
where BE is the unit ball of E, g 2 E+, and 0 < / 1, is mean ergodic and its fixed
space Fix(T) is finite dimensional. This generalizes the main result of [12]. Moreover,
under the assumption that E is a -Dedekind complete Banach lattice, we prove that
if, for any positive power bounded operator T, the condition () implies that T is
mean ergodic then E is a KB-space.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/12607213/index.pdf |
| Date | 01 June 2006 |
| Creators | Binhadjah, Ali Yaslam |
| Contributors | Alpay, Safak Ahmed |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | Ph.D. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for public access |
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