An extension of the Koplienko-Neidhardt trace formulae

Koplienko (Sibirsk. Mat. Zh. 25(5) (1984) 62) found a trace formula for perturbations of self-adjoint operators by operators of Hilbert Schmidt class S2. A similar formula in the case of unitary operators was obtained by Neidhardt (Math. Nachr. 138 (1988) 7). In this paper we improve their results and obtain sharp conditions under which the Koplienko-Neidhardt trace formulae hold.