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Graduate Texts in Mathematics

An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space

Authors: Schmüdgen, Konrad

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  • 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
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  • ISBN 978-3-030-46366-3
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About this Textbook

This textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers.

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.

About the authors

Konrad Schmüdgen is Emeritus Professor at the Mathematical Institute of the University of Leipzig. He has worked for decades on unbounded representations and made important contributions. Among these are trace representation theorems for linear functionals, noncommutative Positivstellensätze, results on the transition probability, the theory of induced and well-behaved representations and classifications results of representations of special classes of algebras. He is the author of several books, including the Graduate Texts in Mathematics Unbounded Self-adjoint Operators on Hilbert Space (2012) and The Moment Problem (2017).

Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook $59.99
price for USA in USD
  • ISBN 978-3-030-46366-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.99
price for USA in USD
  • ISBN 978-3-030-46365-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
285
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-46366-3
DOI
10.1007/978-3-030-46366-3
Hardcover ISBN
978-3-030-46365-6
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XVIII, 381
Number of Illustrations
9 b/w illustrations
Topics

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