AUTOMATIC CONTINUITY OF n-HOMOMORPHISMS BETWEEN TOPOLOGICAL ALGEBRAS
| Autor: | Taher Ghasemi Honary, Hamid Shayanpour |
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| Rok vydání: | 2011 |
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| Zdroj: | Bulletin of the Australian Mathematical Society. 83:389-400 |
| ISSN: | 1755-1633 0004-9727 |
| DOI: | 10.1017/s0004972711002036 |
| Popis: | A map θ:A→B between algebras A and B is called n-multiplicative if θ(a1a2⋯an)=θ(a1) θ(a2)⋯θ(an) for all elements a1,a2,…,an∈A. If θ is also linear then it is called an n-homomorphism. This notion is an extension of a homomorphism. We obtain some results on automatic continuity of n-homomorphisms between certain topological algebras, as well as Banach algebras. The main results are extensions of Johnson’s theorem to surjective n-homomorphisms on topological algebras, a theorem due to C. E. Rickart in 1950 to dense range n-homomorphisms on topological algebras and two theorems due to E. Park and J. Trout in 2009 to * -preserving n-homomorphisms on lmc * -algebras. |
| Databáze: | OpenAIRE |
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