Common fixed points of holomorphic mappings and retracts of B∞H

If B-H(infinity) is the open unit ball in a Cartesian product of infinitely many Hilbert spaces with the sup norm and {r(n)}(nis an element ofN) is a sequence of holomorphic retractions of B-H(infinity) with a nonempty common fixed point set Fix({r(n)}(nis an element ofN)) and r(n+1)(B-H(infinity)) subset of r(n)(B-H(infinity)) for every n is an element of N, then the set Fix({r(n)}(nis an element ofN)) is a k(BH)infinity-nonexpansive retract of B-H(infinity).