Abstract
A synaptic algebra is both a special Jordan algebra and a spectral order-unit normed space satisfying certain natural conditions suggested by the partially ordered Jordan algebra of bounded Hermitian operators on a Hilbert space. The adjective “synaptic”, borrowed from biology, is meant to suggest that such an algebra coherently “ties together” the notions of a Jordan algebra, a spectral order-unit normed space, a convex effect algebra, and an orthomodular lattice.
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Communicated by Anatolij Dvurečenskij
Dedicated to Dr. Sylvia Pulmannová on the occasion of her 70th birthday
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Foulis, D.J. Synaptic algebras. Math. Slovaca 60, 631–654 (2010). https://doi.org/10.2478/s12175-010-0037-3
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DOI: https://doi.org/10.2478/s12175-010-0037-3
2000 Mathematics Subject Classification
Keywords
- spectral order-unit normed space
- special Jordan algebra
- convex effect algebra
- orthomodular lattice
- generalized Hermitian algebra
- convex effect algebra
- projections
- square roots
- carriers
- absolute value
- polar decoposition
- quadratic mapping
- Sasaki mapping
- invertible element
- regular element
- simple element
- spectral resolution
- spectrum