Overview
- Describes a new theory, with potential applications to related branches of functional analysis and quantum mechanics
- Covers operator algebraic aspects of the theory as well as its physical applications
- Proves all results in detail, with the operator algebraic basics included in an appendix
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2285)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (5 chapters)
-
Front Matter
-
Back Matter
Keywords
About this book
It begins by building the foundations of the theory of T*-algebras and CT*-algebras, presenting the major results and investigating the relationship between the operator and vector representations of a CT*-algebra. It is then shown via the representation theory of locally convex*-algebras that this theory includes Tomita–Takesaki theory as a special case; every observable algebra can be regarded as an operator algebra on a Pontryagin space with codimension 1. All of the results are proved in detail and the basic theory of operator algebras on Hilbert space is summarized in an appendix.
The theory of CT*-algebras has connections with many other branches of functional analysis and with quantum mechanics. The aim of this book is to make Tomita’s theory available to a wider audience, with the hope that it will be used by operatoralgebraists and researchers in these related fields.
Reviews
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Tomita's Lectures on Observable Algebras in Hilbert Space
Authors: Atsushi Inoue
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-68893-6
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 2021
Softcover ISBN: 978-3-030-68892-9Published: 03 March 2021
eBook ISBN: 978-3-030-68893-6Published: 01 March 2021
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 190
Number of Illustrations: 1 b/w illustrations
Topics: Functional Analysis, Operator Theory, Algebra, Mathematical Physics