Hilbert C*- Modules and Quantum Markov Semigroups

Beschreibung

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 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.

Provides detailed explanation of the basic theory of Hilbert C*-Module Includes wide-ranging applications, from generalized index to module framework Characterizes the Beurling-Deny criterion between operator valued Dirichlet forms and quantum Markov semigroups

Autor*in

Lunchuan Zhang

Themen in »Hilbert C*- Modules and Quantum Markov Semigroups«

Hilbert C*-modules bounded module mappings KSGNS-construction Kasprove’s stablilsation theorem generalized Fredholm module operators quantum Markov semigroups operator-valued Dirichlet forms Stone’s type theorem spectrum decomposition Beurling-Deny criterion

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“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) 

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