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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Universal state space embeddability
of Jordan-Banach algebras


Author: Jan Hamhalter
Journal: Proc. Amer. Math. Soc. 127 (1999), 131-137
MSC (1991): Primary 46L70, 46L50, 28B15, 81P10
MathSciNet review: 1610905
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Abstract: We study extensions of states between projection structures of JB algebras and generalized orthomodular posets. It is shown that projection orthoposet of a JB algebra $A$ admits the universal extension property if and only if the Gleason theorem is valid for $A$. As a consequence we get that any positive Stone algebra-valued measure on projection lattice of a quotient of a JBW algebra without type $I_2$ direct summand extends to a positive measure on an arbitrary larger generalized orthomodular lattice.


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Additional Information

Jan Hamhalter
Affiliation: Permanent address: Czech Technical University–El.Eng., Department of Mathematics, 166 27 Prague 6, Czech Republic; Temporary address: Mathematical Institute, University of Erlangen–Nűrnberg, Bismarkstrasse 1 1/2, D 910 54 Erlangen, Germany
Email: hamhalte@math.feld.cvut.cz, hamhal@mi.uni-erlangen.de

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04919-9
PII: S 0002-9939(99)04919-9
Keywords: Jordan algebras, extensions of measures on projections, generalized orthomodular posets, Gleason theorem
Received by editor(s): May 1, 1997
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society