ALMOST MULTIPLICATIVE LINEAR FUNCTIONALS AND ENTIRE FUNCTIONS

Let T be a unital, continuous linear functional defined on complex Banach algebra A. First, we prove an approximate version of the Gleason-Kahane-Zelazko theorem: given is an element of > 0, there exists an M > 0 such that, if T(exp x) not equal 0, x is an element of A, parallel to x parallel to <= M, then T is &almost multiplicative. Then, we show that this result remains true if the exponential function is replaced by a nonsurjective entire function F with F'(0) not equal 0.