Let X be a compact Hausdorff topological space. The Banach space C(X) consists of all
continuous complex value functions with the supnorm. An operator P on C(X) is called a
generalized bicircular projection if P + £f(I − P) is an isometry for all |£f| = 1, £f in C and
P2 = P.
In this thesis, we study some projections which are the averages of two composition
operators or two weighted composition operators on C(X). If a projection is the average of
the identity and a composition operator, it is a generalized bicircular projection. And give
an example of a projection which is the average of the identity and a weighted composition
operator, but not a generalized bicircular projection.
We also discuss some projections which are the average of two bounded linear operators
on a Banach space. And the main result is that, let T1 and T2 are two bounded linear
operators on a Banach space, and Q = T1+T2
2 . If T1 ¡CT2 = T2 ¡CT1 and T2
1 = T2
2 = Id then Q
is a tripotent, i.e. Q3 = Q.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0708109-151750 |
| Date | 08 July 2009 |
| Creators | Liu, Chih-Neng |
| Contributors | Pei-Yuan Wu, Hwa-Long Gau, Chao-Liang Shen, Ngai-Ching Wong, Su-Jane Yu |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0708109-151750 |
| Rights | not_available, Copyright information available at source archive |
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