On the Nonexistence of Nontrivial Involutive n-Homomorphisms of C*-algebras
| dc.creator | Park, Efton | |
| dc.creator | Trout, Jody | |
| dc.date | 2007-04-06 | |
| dc.date | 2007-09-27 | |
| dc.date.accessioned | 2026-07-07T08:32:11Z | |
| dc.date.available | 2026-07-07T08:32:11Z | |
| dc.description | An n-homomorphism between algebras is a linear map $ϕ: A \to B$ such that $ϕ(a_1 ... a_n) = ϕ(a_1)... ϕ(a_n)$ for all elements $a_1, >..., a_n \in A.$ Every homomorphism is an n-homomorphism, for all n >= 2, but the converse is false, in general. Hejazian et al. [7] ask: Is every *-preserving n-homomorphism between C*-algebras continuous? We answer their question in the affirmative, but the even and odd n arguments are surprisingly disjoint. We then use these results to prove stronger ones: If n >2 is even, then $ϕ$ is just an ordinary *-homomorphism. If n >= 3 is odd, then $ϕ$ is a difference of two orthogonal *-homomorphisms. Thus, there are no nontrivial *-linear n-homomorphisms between C*-algebras. | |
| dc.description | 13 pages; final version to appear in Transactions of the AMS | |
| dc.identifier | https://arxiv.org/abs/0704.0910 | |
| dc.identifier | http://arxiv.org/abs/0704.0910 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138719 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L05 (Primary); 47B99, 47L30 (Secondary) | |
| dc.title | On the Nonexistence of Nontrivial Involutive n-Homomorphisms of C*-algebras | |
| dc.type | text |