Semiconstant measures on hyperbolic logics
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- by Marjan Matvejchuk PDF
- Proc. Amer. Math. Soc. 125 (1997), 245-250 Request permission
Abstract:
We characterize the set of all semiconstant measures on the hyperbolic logics of projections in indefinite metric spaces and describe the set of all probability measures on these logics.References
- George W. Mackey, The mathematical foundations of quantum mechanics: A lecture-note volume, W. A. Benjamin, Inc., New York-Amsterdam, 1963. MR 0155567
- Andrew M. Gleason, Measures on the closed subspaces of a Hilbert space, J. Math. Mech. 6 (1957), 885–893. MR 0096113, DOI 10.1512/iumj.1957.6.56050
- K. Yu. Dadashyan and S. S. Khoruzhiĭ, Field algebras in quantum theory with indefinite metric, Teoret. Mat. Fiz. 54 (1983), no. 1, 57–77 (Russian, with English summary). MR 704009
- M. S. Matveĭchuk, Measures on the quantum logic of subspaces of a $J$-space, Sibirsk. Mat. Zh. 32 (1991), no. 2, 104–112, 212 (Russian); English transl., Siberian Math. J. 32 (1991), no. 2, 265–272. MR 1138445, DOI 10.1007/BF00972773
- T. Ya. Azizov and I. S. Iokhvidov, Linear operators in spaces with an indefinite metric, Pure and Applied Mathematics (New York), John Wiley & Sons, Ltd., Chichester, 1989. Translated from the Russian by E. R. Dawson; A Wiley-Interscience Publication. MR 1033489
- M. S. Matveĭchuk, Description of indefinite measures on $W^\ast J$-factors, Dokl. Akad. Nauk SSSR 319 (1991), no. 3, 558–561 (Russian); English transl., Soviet Math. Dokl. 44 (1992), no. 1, 161–165. MR 1148972
Additional Information
- Marjan Matvejchuk
- Affiliation: Department of Mechanics and Mathematics, Kazan State University, 18 Lenin St., 420008, Kazan, Russia
- Email: marjan@niimm.kazan.su
- Received by editor(s): February 14, 1994
- Received by editor(s) in revised form: July 13, 1995
- Additional Notes: Supported by The Russian Foundation for Fundamental Research, grant no. 93-011-16099.
- Communicated by: J. Marshall Ash
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 245-250
- MSC (1991): Primary 81P10, 46L50, 46B09, 46C20, 03G12; Secondary 28A60
- DOI: https://doi.org/10.1090/S0002-9939-97-03591-0
- MathSciNet review: 1350955