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States on families of subspaces of pre-Hilbert spaces |
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| Authors: | Anatolij Dvurečenskij |
| Affiliation: | (1) Mathematical Institute, Slovak Academy of Sciences, Obrancov mieru 49, CS-814 73 Bratislava, Czechoslovakia |
| Abstract: | We present six families of closed subspaces of a pre-Hilbert space and we show that if arbitrary, one of them possesses at least one completely additive state, then the pre-Hilbert space is complete. |
| Keywords: | 46C10 03G12 81B10 |
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