Toeplitz-Composition C*-Algebras for certain finite blaschke products

Hiroyasu Hamada, Yasuo Watatani

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)2113-2123
Number of pages11
JournalProceedings of the American Mathematical Society
Volume138
Issue number6
DOIs
Publication statusPublished - Jun 1 2010

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Blaschke Product
Otto Toeplitz
Algebra
C*-algebra
Composition Operator
Mathematical operators
Chemical analysis
Complex Dynamical Systems
Julia set
Toeplitz Operator
Compact Operator
Hardy Space
Quotient
Isomorphic
Dynamical systems

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Toeplitz-Composition C*-Algebras for certain finite blaschke products. / Hamada, Hiroyasu; Watatani, Yasuo.

In: Proceedings of the American Mathematical Society, Vol. 138, No. 6, 01.06.2010, p. 2113-2123.

Research output: Contribution to journalArticle

Hamada, Hiroyasu ; Watatani, Yasuo. / Toeplitz-Composition C*-Algebras for certain finite blaschke products. In: Proceedings of the American Mathematical Society. 2010 ; Vol. 138, No. 6. pp. 2113-2123.
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