Titlebook: Partial *- Algebras and Their Operator Realizations; Jean-Pierre Antoine,Atsushi Inoue,Camillo Trapani Book 2002 Springer Science+Business

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Unbounded Linear Operators in Hilbert Spaceslbert space. In Section 1.1, we recall the definitions of C*-algebras and von Neumann algebras. In Section 1.2, we define and investigate the notion of closedness, the closure and the adjoint of an unbounded linear operator in a Hilbert space. Section 1.3 is devoted to the Cayley transform approach

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Partial O*-AlgebrasSection 2.1 introduces of O- and O*-families, O- and O*-vector spaces, partial O*-algebras and O*-algebras. Partial O*-algebras and strong partial O*-algebras are defined by the weak and the strong multiplication. Section 2.2 describes four canonical extensions (closure, full-closure, adjoint, biadj

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Topologies on Partial O*-AlgebrasSection 4.1, we compare the graph topologies induced by different O-families on the same domain (and the corresponding families of bounded subsets). In the case where the domain .. of an O-family M is a (quasi-) Fréchet space, the structure of bounded subsets in .. can be described in a rather expli