Regular elements in generalized hermitian algebras
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AbstractA generalized Hermitian (GH) algebra is a special Jordan algebra that is at the same time a spectral order-unit space. In this paper we characterize the von Neumann regular elements in a GH-algebra, relate maximal pairwise commuting subsets of the algebra to blocks in its projection lattice, and prove a Gelfand-Naimark type representation theorem for commutative GH-algebras.
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2017 ◽
Vol 16
(11)
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pp. 1750201
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2019 ◽
Vol 18
(07)
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pp. 1950128
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2019 ◽
pp. 87-100
2012 ◽
Vol 19
(spec01)
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pp. 1017-1040
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2009 ◽
Vol 08
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pp. 601-615
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2011 ◽
Vol 39
(9)
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pp. 3242-3252
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