Abstract. The Gleason--Kahane--Żelazko theorem states that a linear functional on a Banach algebra that is non-zero on invertible elements is necessarily a scalar multiple of a character. Recently this theorem has been extended to certain Banach function spaces that are not algebras. In this article we present a brief survey of these extensions.
AMS Subject Classification
(1991): 15A86; 30H10, 46H05, 46H40, 47B49
Received November 17, 2017, and in revised form January 25, 2018. (Registered under 73/2017.)