论文信息 - THE GEOMETRY OF THE STATE SPACE

THE GEOMETRY OF THE STATE SPACE

Publisher Summary This chapter presents a functional analytic frame for dealing with questions concerning state spaces of orthomodular posets and Dacey manuals. It present examples of orthomodular posets whose state space, a Banach space in the base-norm, is not reflexive. It also presents the appropriate level of generality for an extended measure theory that not only include all the classical cases but also those arising through von Neumann algebras. The chapter highlights the geometrical features of the state space, considered as a base-normed space, and its dual, which is an order unit-normed space. Using the theorem of James, the chapter explains that the state space of an orthomodular poset is reflexive and that state spaces are, in general, not reflexive. It also explains the various states of orthomodular poset.

Hans R. Fischer | Gottfried T. Rüttimann | G. Rüttimann | H. Fischer

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