Similarity of analytic Toeplitz operators on the Bergman spaces (Q971794)

The authors give a function theoretic similarity classification for the Toepltz operators on weighted Bergman space over the unit disk whose symbols are analytic on the closure of the unit disk. The main result states that \(T_f\) is similar to \(T_g\) if and only if there are two finite Blaschke products \(B\) and \(B_1\) with the same finite order and a function \(h\) analytic on the closure of the unit disk such that \(f= h \circ B\) and \(g = h \circ B_1\).