Let be a Banach algebra, and let be a left Banach -module. In this paper, using the notation of point multipliers on left Banach modules, we introduce a certain type of spectrum for the elements of and we also introduce a certain subset of which behaves as the set of invertible elements of a commutative unital Banach algebra. Among other things, we use these sets to give some Gleason–Kahane–Żelazko theorems for left Banach -modules.
"Point multipliers and the Gleason–Kahane–Żelazko theorem." Banach J. Math. Anal. 11 (4) 864 - 879, October 2017. https://doi.org/10.1215/17358787-2017-0021