# Functional Analysis, Linear Structures and Applications Seminar

### $C^\ast$-algebras of Bergman type operators with piecewise slowly oscillating coefficients

Given a simply connected domain $U$ in the complex plane with a piecewise Dini-smooth boundary which admits a finite set of Dini-smooth corners, we study the $C^\ast$-algebra $B_U$ generated by the Bergman and anti-Bergman projections acting on the Lebesgue space $L^2(U)$ and by the operators of multiplication by piecewise continuous functions that slowly oscillate at points of the domain boundary. Applying the Allan-Douglas local principle, the limit operators techniques and the Kehe Zhu results on $\operatorname{VMO}_{\partial}$ functions, we construct a Fredholm symbol calculus for the $C^\ast$-algebra $B_U$ and establish a Fredholm criterion for the operators $A\in B_U$.

The talk is based on joint work with E. Espinoza-Loyola.

Current organizers: Helena Mascarenhas, Ângela Mestre.