Operational Quantum Physics

Busch, Paul; Grabowski, Marian; Lahti, Pekka

doi:10.1007/978-3-540-49239-9

Cited by 611 publications

(885 citation statements)

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“…Effect algebras (EAs in short) were introduced in [8] as an abstract generalization of the Hilbert space effects, that is, self-adjoint operators between the zero and identity operators, which play an important role in the theory of quantum mechanical measurements [3]. Alternative structures called difference posets (D-posets), which are categorically equivalent with effect algebras, were introduced in [17].…”

Section: Introductionmentioning

confidence: 99%

Riesz ideals in generalized effect algebras and in their unitizations

Pulmannová

Vinceková

2007

Algebra univers.

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We show that quotients of generalized effect algebras by Riesz ideals preserve some important special properties, e.g., homogeneity and hereditary Riesz decomposition properties; moreover, quotients of generalized orthoalgebras, weak generalized orthomodular posets, generalized orthomodular lattices and generalized MV-algebras with respect to Riesz ideals belong to the same class. We give a necessary and sufficient condition under which a Riesz ideal I of a generalized effect algebra P is a Riesz ideal also in the unitization E of P . We also study relations between Riesz ideals and central elements in GEAs and in their unitizations. In the last section, we demonstrate the notion of Riesz ideals by some illustrative examples.

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Section: Introductionmentioning

confidence: 99%

Riesz ideals in generalized effect algebras and in their unitizations

Pulmannová

Vinceková

2007

Algebra univers.

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“…They correspond to yes-no measurements that can be unsharp. For detailed explanations we refer to [2] and [5]. In the Hilbert space formalism they are represented by linear bounded self-adjoint operators A : H → H which satisfy 0 ≤ A ≤ I .…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%