C∗–algebras of Bergman Type Operators with Continuous Coefficients on Polygonal Domains

  • YURI I. KARLOVICH
  • Published 2015

Abstract

Given α ∈ (0,2] , the C∗ -algebra AKα generated by the identity operator and by the Bergman and anti-Bergman projections acting on the Lebesgue space L(Kα) over the open sector Kα = { z = reiθ : r > 0, θ ∈ (0,πα) is studied. Then, for any bounded polygonal domain U , the C∗ -algebra BU generated by the operators of multiplication by continuous functions on the closure U of U and by the Bergman and anti-Bergman projections acting on the Lebesgue space L2(U) is investigated. Symbol calculi for the C∗ -algebras AKα and BU are constructed and an invertibility criterion for operators A ∈ AKα and a Fredholm criterion for the operators B ∈ BU in terms of their symbols are established. Mathematics subject classification (2010): Primary 47L15; Secondary 45E10, 47A53, 47G10, 47L30.

Cite this paper

@inproceedings{KARLOVICH2015CalgebrasOB, title={C∗–algebras of Bergman Type Operators with Continuous Coefficients on Polygonal Domains}, author={YURI I. KARLOVICH}, year={2015} }