Which linear maps of the disk algebra are multiplicative
Richard Rochberg · Pacific Journal of Mathematics · 1971
Let T be a linear map of the disk algebra into itself which is of norm one and fixes the constants.This paper considers the question of what additional restrictions suffice to insure that T is multiplicative.It is shown that if T is an isometry and the range of T is a ring then T is multiplicative and that if the image under T of the coordinate function of the disk is an extreme point of the unit ball of the disk algebra then T is multiplicative.