Hilbert C*- Modules and Quantum Markov Semigroups

Erscheinungsjahr 2025
ISBN: 978-981-99-8670-5
Verlag: Springer Nature Singapore

Buch, Englisch, 214 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 347 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Zhang, Lunchuan

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

Inhaltsverzeichnis

Basic Theory of Hilbert C*-modules.- Kasprove’s Stabilization and Fredholm Generalized Index Theory.- Quantum Markov Semigroups and Operator-valued Dirichlet Forms.

Über Autor(innen)

Prof. Lunchuan Zhang received B.S. from Binzhou University in 1983, M.S. from Qufu Normal University in 1994, and Ph.D. from Nanjing University in 1997. He was a post-doctor in Beijing Normal University from 1997 to 1999 and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, from 1999 to 2000. He has joined Renmin University of China since 2000, where he is a Professor at the School of Mathematics currently. His areas of research are quantum probability and quantum stochastic processes.