Cachia V., Zagrebnov V.A. Operator-norm convergence of the Trotter product formula for holomorphic semigroups (39K, LATeX 2e) ABSTRACT. We study the error estimates in operator norm for the Trotter product formula. It is shown that some recent results in this direction can be extended to non-self-adjoint generators and to the case of a Banach space for a class of holomorphic semigroups.