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Further investigation into the properties of the Peirce-one space J1 corresponding to a weak*-closed inner ideal J in a JBW*-triple A is carried out, and, in particular, it is shown that J1 contains no non-trivial weak*-closed ideals.
Abstract. It is shown that there exists a *-homomorphism from the continuous centroid of a JBW*-triple A onto the continuous centroid of an arbitrary weak*-closed inner ideal J in A.
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