Professor Zhang Lunchuan's English Monograph Earns Positive Reviews
Publication Time:2025-10-21
Recently, the English monograph Hilbert C*-Modules and Quantum Markov Semigroups, authored by Professor Zhang Lunzhuan from the School of Mathematics, has attracted wide interest from the global academic community for its contributions to quantum probability. Published by the internationally renowned academic publisher Springer in 2024, the book has received recognition worldwide for its academic value.
The monograph has received high praise and positive recognition from two leading international mathematical reviewing platforms — zbMATH Open (Germany) and Math Reviews (USA).
Review by zbMATH Open (Germany):
Review by Professor Bhat in Math Reviews (USA):
Professor B.V. Rajarama Bhat, a leading expert in quantum probability, also gave the monograph high praise and offered comments on each chapter and the appendix. He noted that the research monograph is distinctive, presenting coherent and innovative contributions to the study of quantum probability. He added that its results can be applied to current hot topics, such as quantum information and quantum computing.
“On the whole one can say that this book presents some specialized topics, especially where the author has made research contributions, from the theory of quantum Markov semigroups. This research monograph will be useful for researchers in that area.”
About Professor Zhang Lunchuan
Professor Zhang Lunchuan, born in 1965, is currently a Professor and doctoral supervisor at the School of Mathematics, Renmin University of China. He began teaching at Renmin University in 1999 and is a member of the Academic Committee of the School of Mathematics, as well as a special reviewer for Math. Reviews. He has also served on the chairing committee of the 6th and 7th Teachers’ Congresses at Renmin University of China.
His main research areas are quantum probability and quantum stochastic processes. He has published over 40 papers in domestic and international core journals, and has authored 8 textbooks (including teaching references) such as Real Variable Functions and Functional Analysis, as well as two research monographs. Among these, his monograph Hilbert C*-Modules and Quantum Markov Semigroups, published in 2024 by Springer, opens a new direction in the study of quantum probability.
Overview of the Monograph
Hilbert C*-Modules and Quantum Markov Semigroups is a major work in the field of quantum probability. The book is divided into three chapters. The first chapter covers the foundational material, providing a detailed introduction to the theory of Hilbert C*-modules. The second chapter covers several major international research topics, including Kasparov’s stability theorem, Morita equivalence theory, generalized index theory, and the theory and applications of module frameworks. The third chapter, which forms the core of the book, develops the theory of module operator semigroups. It establishes a Hille-Yosida-type theorem for infinitesimal generators of module operator semigroups and obtains a quantum Stone theorem within the module framework. The book introduces operator-valued Dirichlet forms, establishes the Beurling-Deny correspondence between operator-valued Dirichlet forms and module operator Markov semigroups, and thereby characterizes the spectral gap properties of infinitesimal generators of quantum Markov semigroups.
