# Two Characterizations of Commutativity for C*-algebra

Abstract (Summary)

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**Bibliographical Information:**