Neidhardt H., Zagrebnov V.A. Trotter-Kato product formula and symmetrically-normed ideals (78K, LATeX) ABSTRACT. It is proven that the Trotter product formula converges in the norm of a symmetrically-normed ideal of compact operators if the Kac operator (the transfer matrix) belongs to this ideal.The reasult is generalized to the Trotter-Kato product formula.