Abstract
In this chapter we will discuss representations of JB-and JBW-algebras as Jordan algebras of self-adjoint operators on a Hilbert space. We will see that there is one crucial difference compared to the situation for C*- algebras: not every JB-algebra admits such a concrete representation. The “Gelfand–Naimark” type theorem (Theorem 4.19) states that there is a certain exceptional ideal, and modulo that ideal every JB-algebra admits a concrete representation, i.e., is a JC-algebra. uch products. SinceKeywordsDirect SummandJordan AlgebraCentral ProjectionFactor RepresentationReal AlgebraThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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