2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70515Koplienko [Ko] found a trace formula for perturbations of self-adjoint operators by operators of Hilbert Schmidt class $\bS_2$. A similar formula in the case of unitary operators was obtained by Neidhardt [N]. In this paper we improve their results and obtain sharp conditions under which the Koplienko--Neidhardt trace formulae hold.21 pagesFunctional AnalysisClassical Analysis and ODEsComplex Variables47A55, 47A63, 47B10, 46E35text