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Abstrakty
We prove that if A is a synaptic algebra and the orthomodular lattice P of projections in A is complete, then A is a factor if and only if A is an antilattice. We also generalize several other results of R. Kadison pertaining to infima and suprema in operator algebras.
Wydawca
Czasopismo
Rocznik
Tom
Strony
1--7
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
- Department of Mathematics and Statistics, University of MassaChusetts, Amherst, MA, 1 Suttn Court, Amherst, MA 01002, USA
autor
- Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-814 73 Bratislava, Slovakia
Bibliografia
- [1] Foulis D. J., Synaptic algebras, Math. Slovaca, 2010, 60, 631-654
- [2] Foulis D. J., Pulmannová S., Projections in a synaptic algebra, Order, 2010, 27, 235-257
- [3] Foulis D. J., Pulmannová S., Type-decomposition of a synaptic algebra, Found. Phys., 2013, 43, 948-968
- [4] Foulis D. J., Pulmannová S., Symmetries in synaptic algebras, Math. Slovaca, 2014, 64, 751-776
- [5] Foulis D. J., Pulmannová S., Commutativity in a synaptic algebra, Math. Slovaca, 2016, 66, 469-482
- [6] Foulis D. J., Pulmannová S., Banach synaptic algebras, Internat. J. Theoret. Phys. (in press), DOI: 10.1007/s10773-017-3641-y
- [7] Foulis D. J., Jenčová A., Pulmannová S., Two projections in a synaptic algebra, Linear Algebra Appl., 2015, 478, 162-187
- [8] Foulis D. J., Jenčová A., Pulmannová S., A projection and an effect in a synaptic algebra, Linear Algebra Appl., 2015, 485, 417-441
- [9] Foulis D. J., Jenčová A., Pulmannová S., Vector lattices in synaptic algebras, Math. Slovaca, 2017, 57, 1509-1524
- [10] Foulis D. J., Jenčová A., Pulmannová S., States and synaptic algebras, Rep. Math. Phys., 2017, 79, 13-32
- [11] Foulis D. J., Jenčová A., Pulmannová S., Every synaptic algebra has the monotone square root property, Positivity, 2017, 21, 919-930
- [12] Foulis D. J., Jenčová A., Pulmannová S., A Loomis-Sikorski theorem and functional calculus for a generalized Hermitian algebra, Rep. Math. Phys., 2017, 80, 255-275
- [13] Pulmannová S., A note on ideals in synaptic algebras, Math. Slovaca, 2012, 62, 1091-1104
- [14] Kadison R. V., Order properties of bounded self-adjoint operators, Proc. Amer. Math. Soc., 1951, 2, 505-510
- [15] Alfsen E. M., Compact Convex Sets and Boundary Integrals, 1st ed., Springer-Verlag, New York, 1971
- [16] McCrimmon K., A taste of Jordan algebras, 1st ed., Springer-Verlag, New York, 2004
- [17] Gudder S., Pulmannová S., Bugajski S., Beltrametti E., Convex and linear effect algebras, Rep. Math. Phys., 1999, 44, 359-379
- [18] Beran L., Orthomodular Lattices, An Algebraic Approach, 1st ed., D. Reidel Publishing Company, Dordrecht, 1985
- [19] Kalmbach G., Orthomodular Lattices, Academic Press, 1st ed., London, New York, 1983
- [20] Foulis D. J., Pulmannová S., Spectral resolution in an order unit space, Rep. Math. Phys., 2008, 62, 323-344
- [21] Gheondea A., Gudder S., Jonas P., On the infimum of quantum effects, J. Math. Phys., 2005, 46
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
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Bibliografia
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