Automatic Continuity of Almost $n$-Multiplicative Linear Functionals

Abstract

We generalize a theorem due to Jarosz, by proving that every almost $n$-multiplicative linear functional on Banach algebra $A$ is automatically continuous. The relation between almost multiplicative and almost $n$-multiplicative linear functional on Banach algebra $A$ is also investigated. Additionally, for commutative Banach algebra $A$, we prove that every almost Jordan homomorphism $\varphi:A\longrightarrow \mathbb{C}$ is an almost $n$-Jordan homomorphism.

Keywords

• almost $n$-multiplicative
• almost $n$-jordan homomorphism
• automatic continuity
• semisimple