Banach Synaptic Algebras |
| |
Authors: | David J Foulis Sylvia Pulmannov |
| |
Institution: | 1.Department of Mathematics and Statistics,University of Massachusetts,Amherst,USA;2.Mathematical Institute,Slovak Academy of Sciences,Bratislava,Slovakia |
| |
Abstract: | Using a representation theorem of Erik Alfsen, Frederic Schultz, and Erling Størmer 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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|