Valentin A. Zagrebnov is an Emeritus Professor of Aix-Marseilles University. He is a member of the Institut de Mathématiques de Marseille - UMR 7373 and its research group on Analysis, Geometry and Topology.

• Semigroups and their generators.- Classes of compact operators.- Trace inequalities.- Gibbs semigroups.- Product formulae for Gibbs semigroups.- Product formulae in symmetrically-normed ideals.- Product formulae in Dixmier ideal.- Appendix A. Spectra of closed operators.- Appendix B. Inequalities in ideals.- Appendix B. More inequalities.-  Appendix C. Kato functions.- Appendix D. Lie-Trotter-Kato product formulae: comments on the bibliography.- Bibliography.- Index

“This well-written and organized book is a reader-friendly manual in the field of Gibbs semigroups. It can be recommended for experts and graduate, postgraduate, and doctoral students.” (Michael Perelmuter, zbMATH 1512.47004, 2023)“The book captures a fascinating snapshot of the current state of Gibbs semigroup theory. The book also provides references to the rich literature, nice historical remarks, and inspiring comments on the topics. It is readable and appropriate for readers who are familiar with the basics of functional analysis and linear operator theory. As such, the book will appeal to students at the senior undergraduate and graduate levels as well as researchers in mathematics and mathematical physics.” (Min He, Mathematical Reviews, June, 2021)