This book explains the basic theory of Hilbert C_-module in detail, covering a wide range of applications from generalized index to module framework. At the center of the book, the Beurling-Deny criterion is characterized between operator valued Dirichlet forms and quantum Markov semigroups, hence opening a new field of quantum probability research. The general scope of the book includes: basic theory of Hilbert C_-modules; generalized indices and module frames; operator valued Dirichlet forms; and quantum Markov semigroups.
This book will be of value to scholars and graduate students in the fields of operator algebra, quantum probability and quantum information.
This book will be of value to scholars and graduate students in the fields of operator algebra, quantum probability and quantum information.
The appendix very briefly covers some of the background material on C_- and von Neumann algebra theory required in the main text. 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. (B. V. Rajarama Bhat, Mathematical Reviews, August 13, 2025)







