Author:
FOULIS DAVID J.,PULMANNOVÁ SYLVIA,VINCEKOVÁ ELENA
Abstract
AbstractEffect algebras, which generalize the lattice of projections in a von Neumann algebra, serve as a basis for the study of unsharp observables in quantum mechanics. The direct decomposition of a von Neumann algebra into types I, II, and III is reflected by a corresponding decomposition of its lattice of projections, and vice versa. More generally, in a centrally orthocomplete effect algebra, the so-called type-determining sets induce direct decompositions into various types. In this paper, we extend the theory of type decomposition to a (possibly) noncommutative version of an effect algebra called a pseudoeffect algebra. It has been argued that pseudoeffect algebras constitute a natural structure for the study of noncommuting unsharp or fuzzy observables. We develop the basic theory of centrally orthocomplete pseudoeffect algebras, generalize the notion of a type-determining set to pseudoeffect algebras, and show how type-determining sets induce direct decompositions of centrally orthocomplete pseudoeffect algebras.
Publisher
Cambridge University Press (CUP)
Reference28 articles.
1. Dimension theory in complete orthocomplemented weakly modular lattices
2. Type-Decomposition of an Effect Algebra
3. [11] Foulis D. J. and Pulmannová S. , ‘Centrally orthocomplete effect algebras’, Algebra Universalis, DOI 10.1007/S00012-010-0100-5.
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