Hyponormal Toeplitz operators on weighted Bergman spaces.

We consider operators acting on a Hilbert space that can be written as the sum of a shift and a diagonal operator and determine when the operator is hyponormal. The condition is presented in terms of the norm of an explicit block Jacobi matrix whose entries are explicitly computable in many applications. We apply this result to the Toeplitz operator with symbol z n + c | z | s acting on certain weighted Bergman spaces and determine for what values of the constant c this operator is hyponormal. Our result strengthens an earlier result by the second author, which in turn addressed a question posed by Fleeman and Liaw in 2019. [ABSTRACT FROM AUTHOR]