Kadison’s antilattice theorem for a synaptic algebra

Foulis, D. J.; Pulmannová, S.

doi:10.1515/dema-2018-0002

Artykuł - szczegóły

Tytuł artykułu

Kadison’s antilattice theorem for a synaptic algebra

Autorzy

Foulis D. J. , Pulmannová S.

Wybrane pełne teksty z tego czasopisma

http://www.degruyter.com/view/j/dema

Identyfikatory

DOI

10.1515/dema-2018-0002

Warianty tytułu

Języki publikacji

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.

Słowa kluczowe

synaptic algebra order unit space Jordan algebra spectral resolution antilattice factor

przestrzeń uporządkowana algebra Jordana rozdzielczość widmowa antykrata czynnik

Wydawca

De Gruyter

Czasopismo

Demonstratio Mathematica

Rocznik

2018

Tom

Vol. 51, nr 1

Strony

1--7

Opis fizyczny

Bibliogr. 21 poz.

Twórcy

autor

Foulis D. J.

foulis@math.umass.edu

Department of Mathematics and Statistics, University of MassaChusetts, Amherst, MA, 1 Suttn Court, Amherst, MA 01002, USA

autor

Pulmannová S.

silvia.pulmannova@mat.savba.sk

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

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-df171063-137c-47b5-8854-fa3f2005e605