Classification of Atomic Facially Symmetric Spaces

Abstract A Banach space satisfying some physically significant geometric properties is shown to be the predual of a JBW * –triple. If one considers the unit ball of this Banach space as the state space of a physical system, the result shows that the set of observables is equipped with a natural ternary algebraic structure. This provides a spectral theory and other tools for studying the quantum mechanical measuring process

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