Geodesic
Properties of Topological Measures on Classes of Subspaces of an Inner Product Space
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematics of Quantum Technologies, Tome 313 (2021), pp. 245-252.

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We study topological measures on classes of subspaces of an inner product space. The existence of topological measures is discussed, and their relation to measures on orthoprojections from $\mathcal {B}(H)^{\mathrm{pr}}$ is considered, where $H$ is the completion of the inner product space in question. We also find properties of topological measures defined on classes of splitting and (co)complete subspaces of an inner product space. 
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V. I. Sukharev; E. A. Turilova. Properties of Topological Measures on Classes of Subspaces of an Inner Product Space. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematics of Quantum Technologies, Tome 313 (2021), pp. 245-252. http://geodesic.mathdoc.fr/item/TM_2021_313_a19/

[1] Amemiya I., Araki H., “A remark on Piron's paper”, Publ. Res. Inst. Math. Sci. Kyoto Univ. Ser. A, 2 (1966), 423–427 | DOI | MR | Zbl

[2] Dvurečenskij A., “Regular measures and inner product spaces”, Int. J. Theor. Phys., 31:5 (1992), 889–905 | DOI | MR

[3] Dvurečenskij A., Gleason's theorem and its applications, Kluwer, Dordrecht, 1993 | MR | Zbl

[4] Gross H., Keller H.A., “On the definition of Hilbert space”, Manuscr. math., 23 (1977), 67–90 | DOI | MR | Zbl

[5] Gudder S., “Inner product spaces”, Amer. Math. Mon., 81 (1974), 29–36 | DOI | MR | Zbl

[6] Hamhalter J., Quantum measure theory, Kluwer, Dordrecht, 2003 | MR | Zbl

[7] Hamhalter J., Pták P., “A completeness criterion for inner product spaces”, Bull. London Math. Soc., 19 (1987), 259–263 | DOI | MR | Zbl

[8] J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton Univ. Press, Princeton, NJ, 2018 | MR | Zbl

[9] Turilova E., “Measures on classes of subspaces affiliated with a von Neumann algebra”, Int. J. Theor. Phys., 48:11 (2009), 3083–3091 | DOI | MR | Zbl