The central kernel of the Peirce-one space
Any weak*-closed inner ideal of a JBW*-triple \(A\) enjoys the generalized Peirce decomposition \(A=J_0\oplus J_1\oplus J_2\), where \(J_2=J\) and \(J_0\) (the annihilator of \(J)\) are weak*-closed inner ideals of \(A\), and \(J_1\) is a weak*-closed subspace of \(A\), but it is not, in general, even a subtriple of \(A\). The main result of the paper proves that, in fact, \(J_1\) does not contain non-zero weak*-closed ideals of \(A\).
scientific article; zbMATH DE number 2051619