Numerical range of Toeplitz and weighted composition operators on weighted Bergman spaces

Abstract In this article, we completely describe the numerical range of Toeplitz operators on weighted Bergman spaces with harmonic symbol. We also characterize the numerical range of weighted composition operators on weighted Bergman spaces and classify some sets which are the numerical range of composition operators. We investigate the inclusion of zero in the numerical range, and compute the radius of circular and elliptical disk contained in the numerical range of weighted composition operators on weighted Bergman spaces.