Isometric shifts on (c⊕X)∞

Let c be the set of all convergent sequences with the sup norm and X a strictly convex Banach space. Let Q be the natural projection from (c⊕X)∞ to X and let T be an isometric shift on (c⊕X)∞. We prove the following:(1)The restriction of Q∘T to X is a surjective isometry.(2)T maps c into c and the restriction of T to c is an isometric shift. We also show that the space (c⊕ℓ1)∞ admits an isometric shift.