Overview
- Provides an accessible introduction to basic results and notions of unbounded representation theory
- Contains an extensive study of representations of the Weyl algebra and the commutation relation of quantum mechanics
- Treats many topics in unbounded representation theory in book form for the first time
Part of the book series: Graduate Texts in Mathematics (GTM, volume 285)
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
About this book
The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations and representations on rigged modules.
Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.
Reviews
“This is a fantastic book. The material it covers is wonderful and exciting. The book is well-written, and in fact pleasant to read. It takes a familiar subject --- that is unfortunately not as popular among mathematicians as it should be --- and presents it from a very evocative perspective. Kudos to Schmüdgen.” (Michael Berg, MAA Reviews, July 22, 2023)
“It is very well written, the style is pleasant and attractive, and the information can be used by beginners and by specialists as well. All chapters are accompanied by exercises and pertinent historical comments. … all researchers interested in representation theory may regard this work not only as a reference book but also as a source of inspiration for further development.” (Florian-Horia Vasilescu, zbMATH 1458.47002, 2021)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space
Authors: Konrad Schmüdgen
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-030-46366-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-46365-6Published: 28 July 2020
Softcover ISBN: 978-3-030-46368-7Published: 29 July 2021
eBook ISBN: 978-3-030-46366-3Published: 28 July 2020
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XVIII, 381
Topics: Operator Theory, Mathematical Physics, Associative Rings and Algebras, Topological Groups, Lie Groups