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.
Pacific Journal of Mathematics
Lin, P. (1990). The isometries of H∞(E). Pacific Journal of Mathematics, 143 (1), 69-77. https://doi.org/10.2140/pjm.1990.143.69