
Tomita's Lectures on Observable Algebras in Hilbert Space
Atsushi Inoue(Author)
Springer (Publisher)
Published on 3. March 2021
Book
Paperback/Softback
X, 190 pages
978-3-030-68892-9 (ISBN)
Description
This book is devoted to the study of Tomita's observable algebras, their structure and applications.
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 operator algebraists and researchers in these related fields.
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 operator algebraists and researchers in these related fields.
More details
Product info
Book
Series
Edition
1st ed. 2021
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
1 s/w Abbildung
X, 190 p. 1 illus.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 12 mm
Weight
312 gr
ISBN-13
978-3-030-68892-9 (9783030688929)
DOI
10.1007/978-3-030-68893-6
Schweitzer Classification
Other editions
Additional editions

E-Book
03/2021
Springer
€58.84
Available for download
Person
Atsushi Inoue is a professor emeritus of Fukuoka University. He has researched unbounded operator algebras and unbounded *-representations of (locally convex) *-algebras (bibliography: A. Inoue, Tomita-Takesaki Theory in Algebras of Unbounded Operators, Springer-Verlag, Berlin, 1998; J-P. Antoine, A. Inoue and C. Trapani, Partial *-Algebras and Their Operator Realizations, Math. Appl. 553, Kluwer Academic, Dordrecht, 2002 and about 100 papers)
Content
Introduction.- Fundamentals of Observable Algebras.- Density Theorems.- Structure of CT*-algebras.- Applications.