The isometries of H^∞(E)

Pei-Kee Lin

Vol. 143 (1990), No. 1, 69–77

DOI: 10.2140/pjm.1990.143.69

Abstract

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

where 𝒯 is an isometry from E onto E and t is a conformal map of the unit disc onto itself.

Mathematical Subject Classification 2000

Primary: 46J15

Secondary: 46E40

Milestones

Received: 3 June 1988

Published: 1 May 1990