ebook9783030688936d4325

Description

‚ÄãThis 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‚ÄìTakesaki 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‚Äôs theory available to a wider audience, with the hope that it will be used by operatoralgebraists and researchers in these related fields.¬†