Abstract
If A is a unital complex Banach algebra, and if sigma(a) denotes the spectrum of an element a is an element of A, then the famous Gleason-Kahane-Zelazko Theorem says that any linear functional phi : A -> C satisfying phi(a) is an element of sigma(a) for each a is an element of A, is multiplicative and continuous. In this paper we establish a multiplicative Gleason-Kahane-Zelazko theorem for the case where A is a C-star-algebra. Specifically, if A is a C-star-algebra, then any continuous multiplicative functional phi : A -> C satisfying phi(a) is an element of sigma( a) for each a is an element of A, is linear and hence a character of A. (C) 2021 Elsevier Inc. All rights reserved.