Open Problems for Sequential Effect Algebras

Open Problems for Sequential Effect Algebras

A sequential effect algebra (SEA) is an effect algebra on which a sequential product with certain natural properties is defined. In such structures, we can study combinations of simple measurements that are series as well as parallel. This article presents some open problems for SEAs together with b...

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Veröffentlicht in:International journal of theoretical physics 2005-12, Vol.44 (12), p.2199-2206
1. Verfasser: Gudder, Stan
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Hilbert space
Set theory
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Zusammenfassung:A sequential effect algebra (SEA) is an effect algebra on which a sequential product with certain natural properties is defined. In such structures, we can study combinations of simple measurements that are series as well as parallel. This article presents some open problems for SEAs together with background material, comments and partial results. Two examples of open problems are the following: is A∘ B = A1/2BA1/2 the only sequential product on a Hilbert space SEA? It is known that the sharp elements of a SEA form an orthomodular poset. Is every orthomodular poset isomorphic to the set of sharp elements for some SEA?
ISSN:0020-7748
1572-9575
DOI:10.1007/s10773-005-8015-1