Projections in the convex hull of three surjective isometries on C(Ω)

Let Ω be a compact connected Hausdorff space. We define generalized n-circular projection on C(Ω) as a natural analogue of generalized bi-circular projection and show that such a projection P can always be represented as where I is the identity operator and T is a surjective isometry on C(Ω) such that Tn=I. We next show that if convex combination of three distinct surjective isometries on C(Ω) is a projection, then it is a generalized 3-circular projection.