INVARIANT INNER IDEALS IN W-ASTERISK-ALGEBRAS

Let H(B, alpha) be the JBW-algebra of elements of a continuous W*-alg ebra B invariant under the -anti-automorphism alpha of B of order two . Then the mapping I - I anb H (B, alpha) is an order isomorphism from the complete lattice of alpha-invariant weak closed inner ideals in B onto the complete lattice of weak closed inner ideals in H (B, alph a), every one of which is of the form eH(B, alpha) alpha(e) for some u nique projection e in B with alpha-invariant central support. A coroll ary of this result completely characterizes the weak closed inner ide als in any continuous JBW-triple.