On Automatic Continuity of 3-Homomorphisms on Banach Algebras

Abstract

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

7 Pages (Minor revision), to appear in Bull. Malays. Math. Sci. Soc

Cited by in corpus (1)

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