Pradhan, Chandan2023-09-122023-10-202023-09-122023-10-202023ROLL NO.186123006https://gyan.iitg.ac.in/handle/123456789/2455Supervisor: Chattopadhyay, ArupThe dissertation gives a new proof of some existing second-order trace formulas, namely the Koplienko-Neidhardt trace formula for pair of unitaries in the multiplicative path, the Koplienko-Neidhardt trace formula for pair of contractions via linear path with one of them being normal. Our proofs are based on the idea of the finite-dimensional approximation method introduced by Voiculescu. As a consequence of our results and the Schaffer matrix unitary dilation, we obtained second-order trace formula for a class of pairs of contractions via linear path. Using a different setup of finite dimensional approximations, we extend the Koplienko-Neidhardt trace formula for a class of pairs of contractions via multiplicative path.enSchatten p-classTrace Formulae in Pertubation TheorySpectral Shift FunctionDouble Operator IntegralsSchaffer Matrix Unitary DilationThesis