Titlebook: Unbounded Operator Algebras and Representation Theory; Konrad Schmüdgen Book 1990 Springer Basel AG 1990 Hilbert space.algebra.field.lie a

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Integral Decompositions of *-Representations and Statesucible *-representations and to decompose a positive linear functional as an integral over pure states. Loosely speaking, for most of our results concerning these problems some nuclearity assumptions play a crucial role. We briefly explain our approach to the first problem. Let . be a *-representati

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Basics of *-Representations-algebra and . preserves the involution, then . is called a *-representation of ?. Though our main intention is the study of *-representations, we need to consider also representations, since, for instance, the adjoint of a *-representation is a representation, but not a *-representation in general.

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Integrable Representations of Enveloping AlgebrasLie algebra g, and let ?(g) be the universal enveloping algebra of the complexification of g. A representation of the *-algebra ?(g) is said to be . if it is equal to the infinitesimal representation d. of some unitary representation . of . When . is connected and simply connected, the .-integrable representations are called simply ..

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