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n-Homomorphisms
Shirin Hejazian,Madjid Mirzavaziri,Mohammad Sal Moslehian +2 more
- 27 Jun 2004
TL;DR: In this article, the authors investigated the relation between homomorphisms and homomorphism and characterized $n$-homomorphisms in terms of homomorphic properties under certain conditions, including continuity and commutativity.
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Abstract: 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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Citations
n -JORDAN HOMOMORPHISMS
TL;DR: In this article, the n -Jordan homomorphisms on Banach algebras were investigated and some results related to continuity were given as well as some results about continuity.
•Journal Article
On Automatic Continuity of 3-Homomorphisms on Banach Algebras
TL;DR: In this article, the authors investigated 3-homomorphisms on Banach algebras with bounded approximate identities and established that every involution preserving homomorphism between C -algebra is norm decreasing.
On the nonexistence of nontrivial involutive "n"-homomorphisms of "C*"-algebras
Efton Park,Jody Trout +1 more
TL;DR: In this article, it was shown that every *-preserving n-homomorphism between C*-algebras is a linear map, and that there are no nontrivial *-linear nhomomorphisms.
A characterisation of 3-jordan homomorphisms on banach algebras
TL;DR: In this paper, it was shown that each 3-Jordan homomorphism between Banach algebras is a 3-homomorphism, under special hypotheses, and that any 3-jordanomorphism is a 2-JH.
17
Characterization of n-Jordan Homomorphisms and Automatic Continuity of 3-Jordan Homomorphisms on Banach Algebras
TL;DR: In this paper, it was shown that every 3-Jordan homomorphism from a Banach algebra into a commutative semisimplex Banach algebra is automatically continuous.
7
References
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Matej Brešar
- 01 Mar 1992
TL;DR: In this article, it was shown that every additive centralizing mapping of a prime ring of characteristic not 2 is not commutative and therefore is not a commuting mapping, and this result holds for any additive mapping.
Rings of Operators on Vector Spaces
TL;DR: In this paper, the authors examined the relationship between ring and space and extended the results of Eidelheit and Mackey to complex spaces and showed that the algebraic properties of the ring of all bounded linear transformations of a real Banach space into itself characterize the space up to an isomorphism.