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URN etd-0611102-083525 Author Chun-Chieh Ko Author's Email Address cokecola@ms7.url.com.tw Statistics This thesis had been viewed 5062 times. Download 2204 times. Department Applied Mathematics Year 2001 Semester 2 Degree Master Type of Document Language zh-TW.Big5 Chinese Title Two Characterizations of Commutativity for C*-algebra Date of Defense 2002-06-07 Page Count 25 Keyword functional calculus characterization C*-algebra commutativity Abstract 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].Advisory Committee Mark C. Ho - chair

Hwa-Long Gau - co-chair

Ngai-Ching Wong - advisor

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etd-0611102-083525.pdf Date of Submission 2002-06-11