TY  - GEN
AB  - 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 TomitaTakesaki 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 Tomitas theory available to a wider audience, with the hope that it will be used by operator algebraists and researchers in these related fields.
AU  - Inoue, Atsushi,
CN  - QA326
CY  - Cham :
DA  - 2021.
DO  - 10.1007/978-3-030-68893-6
DO  - doi
ID  - 1434793
KW  - Operator algebras.
KW  - Hilbert space.
KW  - Algèbres d'opérateurs.
KW  - Espace de Hilbert.
LK  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-68893-6
N2  - 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 TomitaTakesaki 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 Tomitas theory available to a wider audience, with the hope that it will be used by operator algebraists and researchers in these related fields.
PB  - Springer,
PP  - Cham :
PY  - 2021.
SN  - 9783030688936
SN  - 3030688933
T1  - Tomita's lectures on observable algebras in Hilbert space /
TI  - Tomita's lectures on observable algebras in Hilbert space /
UR  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-68893-6
VL  - v. 2285
ER  -