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On States on Orthogonally Closed Subspaces of an Inner Product Space

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Abstract

We show that every finitely additive state on the system F(S) of all orthogonally closed subspaces of an infinite-dimensional inner product space S attains all values from the real interval [0,1]. In particular, we show that there is no finitely additive countably-valued state on F(S) whenever dim S=∞. The main technique we use is an embedding of L(H n ) into F(S).

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Authors and Affiliations

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

    Anatolij Dvurečenskij

  2. Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University, Technická 2, CZ-166 27, Prague 6, Czech Republic

    Pavel PtÁk

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  1. Anatolij Dvurečenskij
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  2. Pavel PtÁk
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Dvurečenskij, A., PtÁk, P. On States on Orthogonally Closed Subspaces of an Inner Product Space. Letters in Mathematical Physics 62, 63–70 (2002). https://doi.org/10.1023/A:1021653216049

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  • DOI: https://doi.org/10.1023/A:1021653216049

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