Marcantognini and Morán obtained the Koplienko-Neidhardt trace formula in [17] for pairs of contractions and pairs of maximal dissipative operators via multiplicative path. In this article, we prove the existence of higher-order spectral shift functions for pairs of contractions and pairs of maximal dissipative operators via multiplicative path by adapting the argument employed in [17].

The authors would like to heartily thank the anonymous referee for a careful reading of the manuscript and several helpful suggestions. The research of the first named author is supported by the Mathematical Research Impact Centric Support (MATRICS) grant, File No :MTR/2019/000640, by the Science and Engineering Research Board (SERB), Department of Science & Technology (DST), Government of India. The second named author gratefully acknowledge the support provided by IIT Guwahati, Government of India.