## Toeplitz operators and related topics

#### Event Title

On Toeplitz operators on poly-Bergman spaces

#### Location

Cupples I Room 215

#### Start Date

7-18-2016 4:00 PM

#### End Date

18-7-2016 4:20 PM

#### Description

We give a new isomorphic description of the poly-Bergman spaces of the upper half-plane $\Pi$, and describe the $C^*$-algebra generated by all Toeplitz operators, acting on each poly-Bergman space, whose symbols depend only on $\theta={\rm arg} \; z$ and have limits values at $\theta=0$ and $\theta=\pi$. This $C^*$-algebra is isomorphic and isometric to the $C^*$-algebra consisting of all matrices $M(x) \in M_n(\mathbb{C}) \otimes C[-\infty,+\infty]$ such that $M(-\infty),M(\infty) \in \mathbb{C} I$.

#### Share

COinS

Jul 18th, 4:00 PM Jul 18th, 4:20 PM

On Toeplitz operators on poly-Bergman spaces

Cupples I Room 215

We give a new isomorphic description of the poly-Bergman spaces of the upper half-plane $\Pi$, and describe the $C^*$-algebra generated by all Toeplitz operators, acting on each poly-Bergman space, whose symbols depend only on $\theta={\rm arg} \; z$ and have limits values at $\theta=0$ and $\theta=\pi$. This $C^*$-algebra is isomorphic and isometric to the $C^*$-algebra consisting of all matrices $M(x) \in M_n(\mathbb{C}) \otimes C[-\infty,+\infty]$ such that $M(-\infty),M(\infty) \in \mathbb{C} I$.