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On Bilinear Forms from the Point of View of Generalized Effect Algebras

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Abstract

We study positive bilinear forms on a Hilbert space which are not necessarily bounded nor induced by some positive operator. We show when different families of bilinear forms can be described as a generalized effect algebra. In addition, we present families which are or are not monotone downwards (Dedekind upwards) σ-complete generalized effect algebras.

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Acknowledgement

The authors are very indebted to anonymous referees for their careful reading and suggestions which helped us to improve the readability of the paper.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Anatolij Dvurečenskij

  2. Depart. Algebra Geom., Palacký Univer., 17. listopadu 12, 771 46, Olomouc, Czech Republic

    Anatolij Dvurečenskij

  3. Depart. of Math. and Statistics, Faculty of Science, Masaryk University, Kotlářská 267/2, 611 37, Brno, Czech Republic

    Jiří Janda

Authors
  1. Anatolij Dvurečenskij
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  2. Jiří Janda
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Correspondence to Jiří Janda.

Additional information

The authors acknowledge the support (A.D.) by the Slovak Research and Development Agency under the contract APVV-0178-11, the grant VEGA No. 2/0059/12 SAV, ESF Project CZ.1.07/2.3.00/20.0051, (J.J.) ESF Project CZ.1.07/2.3.00/20.0051 and Masaryk University grant 0964/2009.

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Dvurečenskij, A., Janda, J. On Bilinear Forms from the Point of View of Generalized Effect Algebras. Found Phys 43, 1136–1152 (2013). https://doi.org/10.1007/s10701-013-9736-2

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  • DOI: https://doi.org/10.1007/s10701-013-9736-2

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