The isometries of H(E)


Let E be a uniformly convex and uniformly smooth complex Banach space. We prove that every onto isometry T on H∞(E) is of the form (TF)(z) = F(F(t(z))) (F ∈ H∞(E), |z| < 1), where F is an isometry from E onto E and t is a conformal map of the unit disc onto itself. © 1990 by Pacific Journal of Mathematics.

Publication Title

Pacific Journal of Mathematics