Titlebook: An Invitation to Unbounded Representations of ?-Algebras on Hilbert Space; Konrad Schmüdgen Textbook 2020 The Editor(s) (if applicable) an

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Prologue: The Algebraic Approach to Quantum Theories,This chapter should be considered as a prologue to the book. It gives a brief and informal introduction to the algebraic approach to quantum theories and provides some physical motivation for the study of general .-representations and states of .-algebras.

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An Invitation to Unbounded Representations of ?-Algebras on Hilbert Space978-3-030-46366-3Series ISSN 0072-5285 Series E-ISSN 2197-5612

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Die kurative ambulante Behandlung,his chapter. The ordering, the orthogonality, and the transition probability of positive linear functionals are investigated in detail. A Radon–Nikodym theorem is proved and the Choquet theory is used to obtain extremal decompositions of states. Finally, quadratic modules are defined by means of .-representations.