# The three types of normal sequential effect algebras

@article{Westerbaan2020TheTT, title={The three types of normal sequential effect algebras}, author={Abraham Westerbaan and Bas Westerbaan and John van de Wetering}, journal={Quantum}, year={2020}, volume={4}, pages={378} }

A sequential effect algebra (SEA) is an effect algebra equipped with a sequential product operation modeled after the Lüders product (a,b)↦aba on C∗-algebras. A SEA is called normal when it has all suprema of directed sets, and the sequential product interacts suitably with these suprema. The effects on a Hilbert space and the unit interval of a von Neumann or JBW algebra are examples of normal SEAs that are in addition convex, i.e. possess a suitable action of the real unit interval on the…

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## References

SHOWING 1-10 OF 69 REFERENCES

Three characterisations of the sequential product

- Mathematics
- 2018

It has already been established that the properties required of an abstract sequential product as introduced by Gudder and Greechie are not enough to characterise the standard sequential product…

Blocks of homogeneous effect algebras

- MathematicsBulletin of the Australian Mathematical Society
- 2001

Effect algebras, introduced by Foulis and Bennett in 1994, are partial algebras which generalise some well known classes of algebraic structures (for example orthomodular lattices, MV algebras,…

Open Problems for Sequential Effect Algebras

- Mathematics
- 2005

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…

Type-Decomposition of an Effect Algebra

- Mathematics
- 2010

Effect algebras (EAs), play a significant role in quantum logic, are featured in the theory of partially ordered Abelian groups, and generalize orthoalgebras, MV-algebras, orthomodular posets,…

Sequential product on standard effect algebra {\cal E} (H)

- Mathematics, Computer Science
- 2009

This paper characterize some algebraic properties of the abstract sequential product of a quantum effect A on a complex Hilbert space H and presents a general method for constructing sequential products on and studies some property of the sequential products constructed by the method.

An Introduction to Effectus Theory

- MathematicsArXiv
- 2015

This text is an account of the basics of effectus theory, which includes the fundamental duality between states and effects, with the associated Born rule for validity of an effect (predicate) in a particular state.

Sequential product on effect logics

- Philosophy
- 2013

In categorical logic predicates on an object X are traditionally represented as subobjects. Jacobs proposes [9] an alternative in which the predicates on X are maps p : X → X + X with [id, id] ◦ p =…

Tensor Product of Distributive Sequential Effect Algebras and Product Effect Algebras

- Mathematics
- 2008

Abstract
A distributive sequential effect algebra (DSEA) is an effect algebra on which a distributive sequential product with natural properties is defined. We define the tensor product of two…