On a theorem of Bishop and commutants of Toeplitz operators in   $\mathbb{C}^n$
  We prove an approximation theorem on a class of domains in $\mathbb{C}^n$ on which the $\overline{\partial}$-problem is solvable in $L^{\infty}$. Furthermore, as a corollary, we obtain a version of the Axler-\v{C}u\v{c}kovi\'c-Rao Theorem in higher dimensions. 
Sonmez Sahutoglu and Akaki Tikaradze
math.CV math.FA