Algebras Generated by the Bergman and Anti-Bergman Projections and by Multiplications by Piecewise Continuous Functions |
| |
Authors: | Yu I Karlovich Luís Pessoa |
| |
Institution: | (1) Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Col. Chamilpa, C.P. 62210 Cuernavaca, Morelos, México;(2) Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049 - 001 Lisboa, Portugal |
| |
Abstract: | The C*-algebra
generated by the Bergman and anti-Bergman projections and by the operators of multiplication by piecewise continuous functions on the Lebesgue space L2(Π) 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 associated with points
and pairs
We construct a symbol calculus for unital C*-algebras generated by n orthogonal projections sum of which equals the unit and by m one-dimensional orthogonal projections. Such algebras are models of local algebras at points z ∈∂Π being the discontinuity points of coefficients. A symbol calculus for the C*- algebra
and a Fredholm criterion for the operators
are obtained. Finally, a C*-algebra isomorphism between the quotient algebra
where
is the ideal of compact operators, and its analogue
for the unit disk is constructed. |
| |
Keywords: | Primary 47A53 47L15 Secondary 47G10 47L30 |
本文献已被 SpringerLink 等数据库收录! |
|