Resumen de Automorphic Composition Operators on Hardy and Bergman Spaces in the Ball

Barbara D. McCluer, Matthew A. Pons

• We determine which composition operators with automorphism symbol are essentially normal on the Hardy and Bergman space of the ball. To do this, we first show that modulo the compact operators, the product of an automorphic composition operator followed by its adjoint is a Toeplitz operator with positive symbol.