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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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