Projections in the Convex Hull of Three Isometries on Absolutely Continuous Function Spaces

Abstract

In this paper, we prove that any projection in the convex hull of three surjective linear isometries on $$\mathrm {AC}(X)$$ is a generalized bi-circular projection, where $$\mathrm {AC}(X)$$ denotes the Banach space of all absolutely continuous functions on a compact subset of $$\mathbb {R}$$ with at least two points. We also show that the trivial projections are the only projections on $$\mathrm {AC}(X)$$ which can be represented as the average of three surjective linear isometries.