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Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero


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CiteScore 2018: 0.47
SCImago Journal Rank (SJR) 2018: 0.265
Source Normalized Impact per Paper (SNIP) 2018: 0.714

Mathematical Citation Quotient (MCQ) 2018: 0.17

ICV 2018: 121.16

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2391-4661
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Volume 51, Issue 1

Issues

Kadison’s antilattice theorem for a synaptic algebra

David J. Foulis
  • Emeritus Professor, Department of Mathematics and Statistics, University of MassaChusetts, Amherst, MA, Postal Adress:1 Suttn Court, Amherst, MA 01002, USA
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/ Sylvia Pulmannová
  • Corresponding author
  • Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-814 73 Bratislava, Slovakia
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Published Online: 2018-03-01 | DOI: https://doi.org/10.1515/dema-2018-0002

Abstract

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.

Keywords: synaptic algebra; order unit space; Jordan algebra; spectral resolution; antilattice; factor

MSC 2010: Primary 46B40; Secondary 46L89

References

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About the article

Received: 2017-09-18

Accepted: 2018-01-19

Published Online: 2018-03-01


Citation Information: Demonstratio Mathematica, Volume 51, Issue 1, Pages 1–7, ISSN (Online) 2391-4661, DOI: https://doi.org/10.1515/dema-2018-0002.

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© 2018 Sylvia Pulmannová and David J. Foulis. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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[2]
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