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A New View of Effects in a Hilbert Space

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Abstract

We investigate certain Brouwer-Zadeh lattices that serve as abstract counterparts of lattices of effects in Hilbert spaces under the spectral ordering. These algebras, called PBZ*-lattices, can also be seen as generalisations of orthomodular lattices and are remarkable for the collapse of three notions of “sharpness” that are distinct in general Brouwer-Zadeh lattices. We investigate the structure theory of PBZ*-lattices and their reducts; in particular, we prove some embedding results for PBZ*-lattices and provide an initial description of the lattice of PBZ*-varieties.

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Correspondence to Francesco Paoli.

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Giuntini, R., Ledda, A. & Paoli, F. A New View of Effects in a Hilbert Space. Stud Logica 104, 1145–1177 (2016). https://doi.org/10.1007/s11225-016-9670-3

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