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Tomita's Lectures on Observable Algebras in Hilbert Space (Paperback, 1st ed. 2021)
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Tomita's Lectures on Observable Algebras in Hilbert Space (Paperback, 1st ed. 2021)
Series: Lecture Notes in Mathematics, 2285
Expected to ship within 10 - 15 working days
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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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