Toeplitz-composition C*-algebras for certain finite Blaschke products
Hiroyasu Hamada, Yasuo Watatani

TL;DR
This paper explores the relationship between composition operators, Toeplitz operators, and complex dynamical systems for finite Blaschke products, revealing a deep algebraic structure linking operator theory and complex dynamics.
Contribution
It establishes an isomorphism between a quotient C*-algebra generated by composition and Toeplitz operators and the C*-algebra of the associated dynamical system, showing it is simple and purely infinite.
Findings
The quotient algebra is isomorphic to the C*-algebra of the dynamical system.
The resulting algebra is simple and purely infinite.
The study connects operator theory with complex dynamical systems.
Abstract
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 C_R on the Hardy space and the C*-algebra associated with the complex dynamical system on the Julia set of R. We study the C*-algebra generated by both the composition operator C_R and the Toeplitz operator T_z to show that the quotient algebra by the ideal of the compact operators is isomorphic to the C*-algebra associated with the complex dynamical system, which is simple and purely infinite.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Operator Algebra Research · Advanced Topics in Algebra
