TY - JOUR
T1 - Toeplitz-Composition C*-Algebras for certain finite blaschke products
AU - Hamada, Hiroyasu
AU - Watatani, Yasuo
N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.
PY - 2010/6
Y1 - 2010/6
N2 - Let R be a finite Blaschke product of degree at least two with R(0) = 0. Then there exists a relation between the associated composition operator Cr on the Hardy space and the C*-algebra Οr(Jr) associated with the complex dynamical system (Ron)n on the Julia set Jr. We study the C*-algebra τCr generated by both the composition operator Cr and the Toeplitz operator Tz to show that the quotient algebra by the ideal of the compact operators is isomorphic to the C*-algebra Οr(Jr), which is simple and purely infinite.
AB - Let R be a finite Blaschke product of degree at least two with R(0) = 0. Then there exists a relation between the associated composition operator Cr on the Hardy space and the C*-algebra Οr(Jr) associated with the complex dynamical system (Ron)n on the Julia set Jr. We study the C*-algebra τCr generated by both the composition operator Cr and the Toeplitz operator Tz to show that the quotient algebra by the ideal of the compact operators is isomorphic to the C*-algebra Οr(Jr), which is simple and purely infinite.
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U2 - 10.1090/S0002-9939-10-10270-6
DO - 10.1090/S0002-9939-10-10270-6
M3 - Article
AN - SCOPUS:77951148105
SN - 0002-9939
VL - 138
SP - 2113
EP - 2123
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 6
ER -