Journal of the
Korean Mathematical Society JKMS

We show various properties of the Berezin operator $T$ and its iteration $T^{k}$ on the $L^{p}$ space of the invariant measure $\tau$ on the complex unit ball $B$ by exhibiting differences between the case of $1 < \ p \ < \infty$ and $p=1, \ \infty$ under the infinite iteration of $T$ or the summation of iterations.

Keywords: Berezin Operator, Berezin transform, invariant measure, invariant Laplacian

MSC numbers: 31B05, 30C05