In this thesis, we characterize the Jacobson radical of the semicrossed product of the disk algebra by an endomorphism which is defined by the composition with a finite Blaschke product. Precisely, the Jacobson radical is the set of those whose 0th Fourier coefficient is identically zero and whose kth Fourier coefficient vanishes on the set of recurrent points of a finite Blaschke product. Moreover, if a finite Blaschke product is elliptic, i.e., it has a fixed point in the open unit disc, then the Jacobson radical coincides with the set of quasinilpotent elements.
|Commitee:||Hansen, Scott, Nordman, Dan, Sacks, Paul, Song, Sung-Yell|
|School:||Iowa State University|
|School Location:||United States -- Iowa|
|Source:||DAI-B 73/10(E), Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Mathematics|
|Keywords:||Disk algebra, Fourier coefficient, Jacobson radical, Semicrossed products|
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