Tomita's Lectures on Observable Algebras in Hilbert Space

Beschreibung

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. 
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 operatoralgebraists and researchers in these related fields. 
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

Autor*in

Atsushi Inoue

Themen in »Tomita's Lectures on Observable Algebras in Hilbert Space«

Decomposition of CT*-algebras Q*-algebras and CQ*-algebras Semisimple (singular) CT*-algebras T*-algebras and CT*-algebras von Neumann (Kaplansky) Type Density Theorem

Stimmen zu »Tomita's Lectures on Observable Algebras in Hilbert Space«

“The text is clearly written and complete proofs of the results are given.” (Mixalis Anoussis, zbMATH 1480.46001, 2022)
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