2011/10/20 by Hamada, Hiroyasu
#37F10 #46L08 #46L55 #47B33 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1110.4426
Let R be a finite Blaschke product. We study the C*-algebra TCR generated by both the composition operator CR and the Toeplitz operator Tz on the Hardy space. We show that the simplicity of the quotient algebra OCR by the ideal of the compact operators can be characterized by the dynamics near the Denjoy-Wolff point of R if the degree of R is at least two. Moreover we prove that the degree of finite Blaschke products is a complete isomorphism invariant for the class of OCR such that R is a finite Blaschke product of degree at least two and the Julia set of R is the unit circle, using the Kirchberg-Phillips classification theorem.