n-Homomorphisms

Details n-Homomorphisms n-Homomorphisms

2004-06-27

arxiv.org/abs/math/0406553v2

Bull. Iranian Math. Soc. 31 (2005), no. 1, 13-23

Mathematics

Functional Analysis

10 pages, revised paper

Scientific paper

Let $\mathcal A$ and $\mathcal B$ be two (complex) algebras. A linear map $\phi:{\mathcal A}\to{\mathcal B}$ is called $n$-homomorphism if $\phi(a_{1}... a_{n})=\phi(a_{1})...\phi(a_{n})$ for each $a_{1},...,a_{n}\in{\mathcal A}.$ In this paper, we investigate $n$-homomorphisms and their relation to homomorphisms. We characterize $n$-homomorphisms in terms of homomorphisms under certain conditions. Some results related to continuity and commutativity are given as well.

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