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Universal state space embeddability of Jordan-Banach algebras
Author(s):
Jan
Hamhalter
Journal:
Proc. Amer. Math. Soc.
127
(1999),
131-137.
MSC (1991):
Primary 46L70, 46L50, 28B15, 81P10
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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  admits the universal extension property if and only if the Gleason theorem is valid for  . As a consequence we get that any positive Stone algebra-valued measure on projection lattice of a quotient of a JBW algebra without type  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--Nurnberg, Bismarkstrasse 1 1/2, D 910 54 Erlangen, Germany
Email:
hamhalte@math.feld.cvut.cz, hamhal@mi.uni-erlangen.de
DOI:
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
Copyright of article:
Copyright
1999,
American Mathematical Society
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