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C*-algebras of poly-Bergman type operators with piecewise continuous coefficients.
by
Yuri Karlovich
Universidad Autónoma del Estado de Morelos, México
Coauthors: Luís Pessoa
The C*-algebra generated by the finite number of poly-Bergman and anti-poly-Bergman projections and by the operators of multiplication by piecewise continuous functions on the Lebesgue space L2 over the upper half-plane is studied. Making use of a local principle, limit operators techniques, and the Plamenevsky results on two-dimensional singular integral operators with coefficients admitting homogeneous discontinuities we reduce the study to simpler C*-algebras. Applying a symbol calculus for the abstract unital C*-algebra generated by a finite number of orthogonal projections sum of which equals the unit and by a finite number of one-dimensional orthogonal projections, we construct a symbol calculus for the initial C*-algebra and obtain a Fredholm criterion for the operators in this C*-algebra.
Date received: March 30, 2005
Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # capg-56.