Unbounded Operator Algebras and Representation Theory

Front Matter....Pages 1-12
Preliminaries....Pages 13-32
Front Matter....Pages 33-34
O-Families and Their Graph Topologies....Pages 35-63
Spaces of Linear Mappings Associated with O-Families and Their Topologization....Pages 64-100
Topologies for O-Families with Metrizable Graph Topologies....Pages 101-122
Ultraweakly Continuous Linear Functionals and Duality Theory....Pages 123-154
The Generalized Calkin Algebra and the *-Algebra % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9 % q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir % -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGa % aeqabaWaaeaaeaaakeaatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0H % gip5wzaGqbciab-jrimnaaCaaaleqabaWaaWbaaWqabeaacqGHRaWk % aaaaaOWaaeWaaeaacqWFdepraiaawIcacaGLPaaaaaa!3E88! $$ {\\mathcal{L}^{^ + }}\\left( \\mathcal{D} \\right)$$ ....Pages 155-174
Commutants....Pages 175-198
Front Matter....Pages 199-200
Basics of *-Representations....Pages 201-235
Self-Adjoint Representations of Commutative *-Algebras....Pages 236-259
Integrable Representations of Enveloping Algebras....Pages 260-299
 n -Positivity and Complete Positivity of *-Representations....Pages 300-329
Integral Decompositions of *-Representations and States....Pages 330-361
Back Matter....Pages 362-380