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arXiv · 1705.01011

Banach synaptic algebras

David J. Foulis·Sylvia Pulmannova
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Abstract

Using a representation theorem of Erik Alfsen, Frederic Schultz, and Erling Stormer for special JB-algebras, we prove that a synaptic algebra is norm complete (i.e., Banach) if and only if it is isomorphic to the self-adjoint part of a Rickart C*-algebra. Also, we give conditions on a Banach synaptic algebra that are equivalent to the condition that it is isomorphic to the self-adjoint part of an AW*-algebra. Moreover, we study some relationships between synaptic algebras and so-called generalized Hermitian algebras.

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David J. Foulis, Sylvia Pulmannova. 2017-05-02. Banach synaptic algebras. https://doi.org/10.1007/s10773-017-3641-y

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