Contractively complemented subspaces of pre-symmetric spaces

We widen significantly the scope of results of Douglas (1965, bounded measurable functions), Arazy-Friedman (1977, bounded operators on Hilbert space) and Kirchberg (1993, von Neumann algebras) by showing that if a subspace X of the predual of a JBW*-triple A is isometric to the predual of another JBW*-triple B, then there is a contractive projection on the predual of A with range X, as long as B does not have a direct summand which is isometric to a space of all essentially bounded measurable functions with values in a Hilbert space of dimension at least two. The result is false without this restriction on B.

(This paper has appeared under the title "Existence of contractive projections on preduals of JBW^*-triples" in Israel J. Math. 182 (2011), 293-331)

ngoz.pdf (286K)

Matthew Neal < nealm@denison.edu >

Bernard Russo < brusso@math.uci.edu >