On Automatic Continuity of 3-Homomorphisms on Banach Algebras

摘要

A linear map $\phi:{\mathcal A}\to {\mathcal B} $ between (Banach) algebrasis called 3-homomorphism if $\phi(abc)=\phi(a)\phi(b)\phi(c)$ for each $a, b, c\in {\mathcal A}$. We investigate 3-homomorphisms on Banach algebras withbounded approximate identities and establish in two ways that every involutionpreserving homomorphism between $C^*$-algebras is norm decreasing.