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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
  • Files
  • etd-0611102-083525.pdf
  • indicate access worldwide
    Date of Submission 2002-06-11

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