A Compact Counterexample to Su\'arez's Berezin Approximation Question
Let $A^2(\mathbb D)$ be the unweighted Bergman space and write $Q_m(S)=T_{B_m(S)}$ for the map induced by the $m$th higher-order Berezin transform. Su\'arez asked in 2005 whether $Q_m(S)$ converges to $S$ in operator norm for every $S$ in the full Bergman Toeplitz algebra. We answer this question negatively in a strong...