Isometries between function algebras with finite codimensional range

Let A be a function algebra on a compact space X. A linear isometry T of A into A is said to be codimension n or finite codimensional if the range of T has codimension n in A. In this paper we prove that such isometries can b e represented as weighted composition mappings on a cofinite subset, (parti al derivative A)(0), of the Shilov boundary for A, partial derivative A. We focus on those finite codimensional isometries for which (partial derivati ve A)(0) = partial derivative A. All the above results, applied to the part icular case of codimension 1 linear isometries on C(X), are used to improve the classification provided by Gutek et al. in J. Funct. Anal. 101, 97-119 (1991).