It is intuitively obvious that if z is a complex number such that ∣1–zv∣ ≤ b ≺ 1 for all positive integers p and some real number b, then z = 1. The purpose of this note is to exhibit a proof of the following generalisation of this observation: THEOREM. Let A be continuous linear operator on a reflexive Banachspace B. If there exists a continuous linear operator T on B, a real number b, and a positive integer p' such that, p an integer and , then A = I. Moreover, in this case ∥I—T∥.