C*-algebras generated by multiplication operators and composition operators with rational symbol
Hiroyasu Hamada

TL;DR
This paper investigates the structure of a C*-algebra generated by multiplication and composition operators associated with a rational function's Julia set, revealing an isomorphism with a dynamical system C*-algebra.
Contribution
It establishes an isomorphism between the C*-algebra generated by multiplication and composition operators and a C*-algebra associated with the rational function's dynamics.
Findings
C*-algebra $\\mathcal{MC}_R$ is isomorphic to $\mathcal{O}_R (J_R)$
The algebra is generated by multiplication operators and a composition operator
Connection between operator algebras and complex dynamical systems
Abstract
Let be a rational function of degree at least two, let be the Julia set of and let be the Lyubich measure of . We study the C-algebra generated by all multiplication operators by continuous functions in and the composition operator induced by on . We show that the C-algebra is isomorphic to the C-algebra associated with the complex dynamical system .
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Taxonomy
TopicsAdvanced Operator Algebra Research · Holomorphic and Operator Theory · Advanced Banach Space Theory
