On inner ideals in ternary algebras. (English) Zbl 0676.46049
Let B be a weak* closed ternary subalgebra of a \(W^*\)-algebra A. If e and f are projections in A such that eBf is a subset of B then eBf is a \(weak^*\) closed inner ideal in B. In terms of the partial isometries in B, a condition is given for pairs (e,f) of projections in A to satisfy \(eBf\subseteq B\). It is shown that for every weak* closed inner ideal J in B there exists a pair (e,f) of projections in A satisfying this condition such that \(J=eBf\). As an application of the main result, a complete description of the weak* closed inner ideals in a continuous \(JBW^*\)-triple having a maximal faithful tripotent is given.
Reviewer: G.T.Rüttimann
MSC:
| 46L70 | Nonassociative selfadjoint operator algebras |
| 46L10 | General theory of von Neumann algebras |
Keywords:
weak\({}^ *\) closed ternary subalgebra of a \(W^ *\)-algebra; \(weak^ *\) closed inner ideals in a continuous \(JBW^ *\)-triple having a maximal faithful tripotentReferences:
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