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Zbl 0932.03072
Gudder, Stanley
$S$-dominating effect algebras. (English)
[J] Int. J. Theor. Phys. 37, No.3, 915-923 (1998). ISSN 0020-7748; ISSN 1572-9575/e

Summary: A special type of effect algebra called an $S$-dominating effect algebra is introduced. It is shown that an $S$-dominating effect algebra $P$ has a naturally defined Brouwer-complementation that gives $P$ the structure of a Brouwer-Zadeh poset. This enables us to prove that the sharp elements of $P$ form an orthomodular lattice. We then show that a standard Hilbert space effect algebra is $S$-dominating. We conclude that $S$-dominating effect algebras may be useful abstract models for sets of quantum effects in physical systems.

MSC 2000:: *03G12 Quantum logic
81P10 Logical foundations of quantum mechanics
06C15 Complemented lattices

Keywords: $D$-posets; $S$-dominating effect algebra; Brouwer-complementation; Brouwer-Zadeh poset; sharp elements; orthomodular lattice; Hilbert space effect algebra

Cited in: Zbl 1155.81012

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