On Automatic Continuity of 3-Homomorphisms on Banach Algebras

Details On Automatic Continuity of 3-Homomorphisms on Banach Algebras On Automatic Continuity of 3-Homomorphisms on Banach Algebras

2006-11-09

arxiv.org/abs/math/0611287v2

Bull. Malays. Math. Sci. Soc. (2) 30(2) (2007), 101--106.

Mathematics

Functional Analysis

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

Scientific paper

A linear map $\phi:{\mathcal A}\to {\mathcal B} $ between (Banach) algebras
is 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 with
bounded approximate identities and establish in two ways that every involution
preserving homomorphism between $C^*$-algebras is norm decreasing.

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