In this thesis, We investigate the problem of when a C*-algebra is commutative through continuous functional calculus, The principal results are that:
(1) A C*-algebra A is commutative if and only if
e^(ix)e^(iy)=e^(iy)e^(ix),
for all self-adjoint elements x,y in A.
(2) A C*-algebra A is commutative if and only if
e^(x)e^(y)=e^(y)e^(x)
for all positive elements x,y in A.
We will give an extension of (2) as follows: Let
f:[a,b]-->[c,d] be any continuous strictly monotonic function where a,b,c,d in R, a<b,c<d. Then a C*-algebra A is commutative if and only if
f(x)f(y)=f(y)f(x),
for all self-adjoint elements x,y in A with spec(x) in [a,b] and spec(y) in [a,b].
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0611102-083525 |
| Date | 11 June 2002 |
| Creators | Ko, Chun-Chieh |
| Contributors | Hwa-Long Gau, Ngai-Ching Wong, Mark C. Ho |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | Cholon |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0611102-083525 |
| Rights | unrestricted, Copyright information available at source archive |
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