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States on Subspaces of Inner Product Spaces with the Gleason Property

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Abstract

We show that the range of every finitely additive state on the system \(\mathcal{F}(E)\) of all orthogonally closed subspaces of an infinite-dimensional inner product space E satisfying the Gleason property is equal to the real interval [0, 1]. Every pre-Hilbert space satisfies the Gleason property, and in Keller spaces it fails to hold.

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Authors and Affiliations

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

    Anatolij Dvurečenskij

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  1. Anatolij Dvurečenskij
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Dvurečenskij, A. States on Subspaces of Inner Product Spaces with the Gleason Property. International Journal of Theoretical Physics 42, 1403–1411 (2003). https://doi.org/10.1023/A:1025771727029

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  • DOI: https://doi.org/10.1023/A:1025771727029

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