# Gleason–Kahane–Żelazko theorem

> theorem that a nonzero linear functional on a unital complex Banach algebra is multiplicative iff it maps each element of the Banach algebra to an element of its spectrum

**Wikidata**: [Q2226660](https://www.wikidata.org/wiki/Q2226660)  
**Source**: https://4ort.xyz/entity/gleason-kahane-elazko-theorem