Abstract

For large classes of complex Banach spaces we consider orbits of finite rank elements under the group of linear isometries. These are real-analytic submanifolds of infinite dimension but of finite CR-codimension. We compute the polynomial convex hull of such orbits $M$ explicitly and show as main result that every continuous CR-function on $M$ has a unique extension to the polynomial convex hull which is holomorphic in a certain sense. This generalizes to infinite dimensions results from a recent joint paper with D. Zaitsev in Inventiones math. 153, 45-104