On inner ideals in ternary algebras
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.
weak\({}^ *\) closed ternary subalgebra of a \(W^ *\)-algebra
\(weak^ *\) closed inner ideals in a continuous \(JBW^ *\)-triple having a maximal faithful tripotent
scientific article; zbMATH DE number 4107478
scientific article