Images of contractive projections on operator algebras (Q1849179)

JW*-triples, that is, weak*-closed subspaces of \(B(H)\) that are also closed under \(x \to xx^{\ast}x\), arise as images of contractive (i.e., norm one) projections on von Neumann algebras. Their generalisations, JBW*-triples, are those complex Banach dual spaces whose open unit balls are bounded symmetric domains. In this paper, the authors investigate the contractive projections on a JBW*-triple. They show that if \(P\) is a weak*-continuous contractive projection on a JBW*-triple \(M\), then \(P(M)\) is of type I or semifinite, respectively, if \(M\) is of the corresponding type. They also show that \(P(M)\) has no infinite spin part if \(M\) is a type I von Neumann algebra.