Skip to main content
SpringerLink
Log in

Weakly Jauch–Piron States in Effect Algebras

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

We study various types of weakly Jauch–Piron states and various types of state-space properties in effect algebras. We generalize several results of Tkadlec (Tatra Mt. Math. Publ. 10, 55–62 1997; Algebra Universalis 61, 187–194 2009) and of Matoušek and Pták (Internat. J. Theoret. Phys. 54, 4476–4481 2015). In particular, we show when an effect algebra is an orthomodular poset, when a unital set of states is strongly order determining, and we present some state space characterizations of Boolean algebras.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structures. Kluwer Academic Publishers, Bratislava (2000). https://doi.org/10.1007/978-94-017-2422-7

    Book  Google Scholar 

  2. Foulis, D.J., Bennett, M.K.: Effect algebras and unsharp quantum logics. Found. Phys. 24, 1331–1352 (1994). https://doi.org/10.1007/BF02283036

    Article  MathSciNet  MATH  ADS  Google Scholar 

  3. Matoušek, M., Pták, P.: Characterization of Boolean algebras in terms of certain states of Jauch–Piron type. Internat. J. Theoret. Phys. 54, 4476–4481 (2015). https://doi.org/10.1007/s10773-015-2638-7

    Article  MathSciNet  MATH  ADS  Google Scholar 

  4. Tkadlec, J.: Conditions that force an orthomodular poset to be a Boolean algebra. Tatra Mt. Math. Publ. 10, 55–62 (1997)

    MathSciNet  MATH  Google Scholar 

  5. Tkadlec, J.: Central elements of effect algebras. Internat. J. Theoret. Phys. 43, 1363–1369 (2004). https://doi.org/10.1023/B:IJTP.0000048621.17418.bb

    Article  MathSciNet  MATH  ADS  Google Scholar 

  6. Tkadlec, J.: Effect algebras with the maximality property. Algebra Universalis 61, 187–194 (2009). https://doi.org/10.1007/s00012-009-0013-3

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the project OPVVV CAAS CZ.02.1.01/0.0/0.0/ 16_019/0000778.

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, CZ–166 27, Praha, Czech Republic

    Josef Tkadlec

Authors
  1. Josef Tkadlec
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Josef Tkadlec.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tkadlec, J. Weakly Jauch–Piron States in Effect Algebras. Int J Theor Phys 60, 865–869 (2021). https://doi.org/10.1007/s10773-020-04709-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-020-04709-5

Keywords

Search

Navigation