Tomita's Lectures on Observable Algebras in Hilbert Space

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 representation...

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Bibliographic Details
Main Author Inoue, Atsushi
Format eBook
LanguageEnglish
Published Cham Springer Nature 2021
Springer International Publishing AG
Springer International Publishing
Edition1
SeriesLecture Notes in Mathematics
Subjects
Algebra
Functional Analysis
Hilbert space
Mathematical Physics
Mathematics
Mathematics and Statistics
Mathematics. Analysis
Operator algebras
Operator Theory
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Summary: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. 
ISBN:9783030688936
3030688933
3030688925
9783030688929
ISSN:0075-8434
1617-9692
DOI:10.1007/978-3-030-68893-6