Products of Toeplitz Operator on the Weighted Bergman Space of the Unit Ball

Abstract:

      We consider the question for what kind of square integrable holomorphic functions $f$, $g$ on the unit ball the densely defined products $T_{f}T_{\bar{g}}$ are invertible and Fredholm on the weighted Bergman space of the unit ball. We furthermore obtain necessary and sufficient conditions for bounded Haplitz products $H_{f}T_{\bar{g}}$, where $f\in L^{2}(B_{n}, \d v_{\alpha})$ and $g$ is a square integrable holomorphic function.