Gleason--Kahane--Żelazko theorems in function spaces

Javad Mashreghi, Thomas Ransford
2018 Acta Scientarum Mathematicarum  
The Gleason-Kahane-\.Zelazko 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.
doi:10.14232/actasm-017-323-8 fatcat:ljng6a75vfghtkwfqmvp5sz7qq