Projections in the convex hull of three surjective isometries on

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 P = I + T + T 2 + ⋯ + T n − 1 n where I is the identity operator and T is a surjective isometry on C ( Ω ) such that T n = 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.