Banach Synaptic Algebras
| Autor: | David J. Foulis, Sylvia Pulmannov |
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| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
46L05 81P05 Quantitative Biology::Neurons and Cognition Physics and Astronomy (miscellaneous) Representation theorem General Mathematics 010102 general mathematics Mathematics - Rings and Algebras 010103 numerical & computational mathematics 01 natural sciences Hermitian matrix Rings and Algebras (math.RA) If and only if Norm (mathematics) FOS: Mathematics 0101 mathematics Algebra over a field Mathematics |
| Zdroj: | International Journal of Theoretical Physics. 57:1103-1119 |
| ISSN: | 1572-9575 0020-7748 |
| DOI: | 10.1007/s10773-017-3641-y |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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