Canonical embedding of an abstract quantum logic into the partial \(Baer^*\)-ring of complex fuzzy events
The author generalizes the known properties of two-valued observables of quantum logic to the notion of complex fuzzy event, that is, a derivable whose spectrum is a subset of the closed complex unit circle, while a fuzzy event is an observable whose spectrum is in [0,1]. The set of all complex fuzzy events is equipped with a structure of partial Baer\({}^*\)-ring in which the set of all the \(Baer^*\)-projections and the set of all the \(Baer^*\)-closed projections are the same and coincide with the set of two-valued observables. The paper is equipped with an example of the Hilbert space quantum logic where the set of all complex fuzzy events corresponds uniquely to the set of all normal operators with spectra in the complex unit circle, and the set of all fuzzy events corresponds one-to-one to the set of all Hermitian operators F with \(0\leq F\leq 1.\)
scientific article; zbMATH DE number 3853073
scientific article