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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 representatio...

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Detalles Bibliográficos
Autor principal: Inoue, Atsushi
Lenguaje:eng
Publicado: Springer 2021
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-030-68893-6
http://cds.cern.ch/record/2758356
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author Inoue, Atsushi
author_facet Inoue, Atsushi
author_sort Inoue, Atsushi
collection CERN
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. .
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spelling cern-27583562021-04-21T16:40:33Zdoi:10.1007/978-3-030-68893-6http://cds.cern.ch/record/2758356engInoue, AtsushiTomita's lectures on observable algebras in Hilbert spaceMathematical Physics and MathematicsThis 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. .Springeroai:cds.cern.ch:27583562021
spellingShingle Mathematical Physics and Mathematics
Inoue, Atsushi
Tomita's lectures on observable algebras in Hilbert space
title Tomita's lectures on observable algebras in Hilbert space
title_full Tomita's lectures on observable algebras in Hilbert space
title_fullStr Tomita's lectures on observable algebras in Hilbert space
title_full_unstemmed Tomita's lectures on observable algebras in Hilbert space
title_short Tomita's lectures on observable algebras in Hilbert space
title_sort tomita's lectures on observable algebras in hilbert space
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-030-68893-6
http://cds.cern.ch/record/2758356
work_keys_str_mv AT inoueatsushi tomitaslecturesonobservablealgebrasinhilbertspace