The following result in the theory of numerical ranges in Banach algebras is well known (see [3, Theorem 12.2]). The numerical range of an element F in the bidual of a unital Banach algebra A is the closure of the set of values at F of the w*-continuous states of . As a consequence of the results in this paper the following

Let G be a locally compact abelian group, let m be a bounded complex-valued Borel measure on G; and let T m be the corresponding convolution operator on L 1 ðGÞ: Let X be a Banach space and let S be a continuous linear operator on X : Then we show that every linear operator F :