Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

On interpolation by analytic maps in infinite dimensions

J. Globevnika1

a1 University of Ljubljana

Abstract

Let A be the complex Banach algebra of all bounded continuous complex-valued functions on the closed unit ball of a complex Banach space X, analytic on the open unit ball, with sup norm. For a class of spaces X which contains all infinite dimensional complex reflexive spaces we prove the existence of non-compact peak interpolation sets for A. We prove some related interpolation theorems for vector-valued functions and present some applications to the ranges of analytic maps between Banach spaces. We also show that in general peak interpolation sets for A do not exist.

(Received May 11 1977)

Footnotes

† This work was supported in part by the Boris Kidrič Fund, Ljubljana, Yugoslavia.