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State on splitting subspaces and completeness of inner product spaces

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Abstract

We show that an inner product spaceV is complete iff the system of all splitting subspaces, i.e., of all subspacesM for whichM + M ⊥=V, possesses at least one completely additive state.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, CS-814 73, Bratislava, Czechoslovakia

    Anatolij Dvurečenskij & Sylvia Pulmannová

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  1. Anatolij Dvurečenskij
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  2. Sylvia Pulmannová
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Dvurečenskij, A., Pulmannová, S. State on splitting subspaces and completeness of inner product spaces. Int J Theor Phys 27, 1059–1067 (1988). https://doi.org/10.1007/BF00674351

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  • DOI: https://doi.org/10.1007/BF00674351

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