Jordan homomorphisms revisited

2008 ◽  
Vol 144 (2) ◽  
pp. 317-328 ◽  
Author(s):  
MATEJ BREŠAR
Keyword(s):  
Commutator Ideal ◽  
Jordan Homomorphism ◽  
Jordan Homomorphisms

AbstractLet θ be a Jordan homomorphism from an algebraAinto an algebraB. We find various conditions under which the restriction of θ to the commutator ideal ofAis the sum of a homomorphism and an antihomomorphism. Algebraic results, obtained in the first part of the paper, are applied to the second part dealing with the case whereAandBareC*-algebras.

A characterization of Jordan and 5-Jordan homomorphisms between Banach algebras

2018 ◽  
Vol 11 (02) ◽  
pp. 1850021 ◽  
Author(s):  
A. Zivari-Kazempour
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Commutative Banach Algebra ◽  
Jordan Homomorphism ◽  
Jordan Homomorphisms ◽  
Unital Banach Algebra

We prove that each surjective Jordan homomorphism from a Banach algebra [Formula: see text] onto a semiprime commutative Banach algebra [Formula: see text] is a homomorphism, and each 5-Jordan homomorphism from a unital Banach algebra [Formula: see text] into a semisimple commutative Banach algebra [Formula: see text] is a 5-homomorphism.

scholarly journals Characterization of $n$-Jordan Homomorphisms on Rings

2021 ◽  
Vol 53 ◽  
Author(s):  
Abbas Zivari-kazempour ◽  
Mohammad Valaei
Keyword(s):  
Jordan Homomorphism ◽  
Jordan Homomorphisms

In this paper, we prove that if $\varphi:\mathcal{R}\longrightarrow\mathcal{R}'$ is an $n$-Jordan homomorphism, where $\mathcal{R}$ has a unit $e$, then the map $a\longmapsto \varphi(e)^{n-2}\varphi(a)$ is a Jordan homomorphism.  As a consequence we show, under special hypotheses, that each $n$-Jordan homomorphism is an $n$-homomorphism.

scholarly journals A Characterization of Bi-Jordan Homomorphisms on Banach Algebras

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
Author(s):  
Abbas Zivari-Kazempour
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Commutative Banach Algebra ◽  
Jordan Homomorphism ◽  
Jordan Homomorphisms

For Banach algebras A and B, we show that if U=A×B is unital and commutative, each bi-Jordan homomorphism from U into a semisimple commutative Banach algebra D is a bihomomorphism.

scholarly journals n-JORDAN HOMOMORPHISMS

2009 ◽  
Vol 80 (1) ◽  
pp. 159-164 ◽  
Author(s):  
M. ESHAGHI GORDJI
Keyword(s):  
Banach Algebras ◽  
Jordan Homomorphism ◽  
Additive Map ◽  
Jordan Homomorphisms

AbstractLet n∈ℕ and let A and B be rings. An additive map h:A→B is called an n-Jordan homomorphism if h(an)=(h(a))n for all a∈A. Every Jordan homomorphism is an n-Jordan homomorphism, for all n≥2, but the converse is false in general. In this paper we investigate the n-Jordan homomorphisms on Banach algebras. Some results related to continuity are given as well.

scholarly journals On Jordan mappings of inverse semirings

2017 ◽  
Vol 15 (1) ◽  
pp. 1123-1131 ◽  
Author(s):  
Sara Shafiq ◽  
Muhammad Aslam
Keyword(s):  
Jordan Derivation ◽  
Jordan Homomorphism ◽  
Jordan Homomorphisms

Abstract In this paper, the notions of Jordan homomorphism and Jordan derivation of inverse semirings are introduced. A few results of Herstein and Brešar on Jordan homomorphisms and Jordan derivations of rings are generalized in the setting of inverse semirings.

scholarly journals Characterization of mixed n-Jordan and pseudo n-Jordan homomorphisms

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 1989-2002
Author(s):  
Masoumeh Neghabi ◽  
Abasalt Bodaghi ◽  
Abbas Zivari-Kazempour
Keyword(s):  
Banach Algebra ◽  
Jordan Homomorphism ◽  
Mild Conditions ◽  
Jordan Homomorphisms ◽  
Semisimple Banach Algebra

In this article, a new notion of n-Jordan homomorphism namely the mixed n-Jordan homomorphism is introduced. It is proved that how a mixed (n + 1)-Jordan homomorphism can be a mixed n-Jordan homomorphism and vice versa. By means of some examples, it is shown that the mixed n-Jordan homomorphisms are different from the n-Jordan homomorphisms and the pseudo n-Jordan homomorphisms. As a consequence, it shown that every mixed Jordan homomorphism from Banach algebra A into commutative semisimple Banach algebra B is automatically continuous. Under some mild conditions, every unital pseudo 3-Jordan homomorphism is a homomorphism.

scholarly journals Stability of -Jordan Homomorphisms from a Normed Algebra to a Banach Algebra

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yang-Hi Lee
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Ring Homomorphism ◽  
Normed Algebra ◽  
Jordan Homomorphism ◽  
Commutative Banach Algebras ◽  
Jordan Homomorphisms

We establish the hyperstability of -Jordan homomorphisms from a normed algebra to a Banach algebra, and also we show that an -Jordan homomorphism between two commutative Banach algebras is an -ring homomorphism.

scholarly journals U- S Jordan Homomorphisim of Inverse Semirings

2019 ◽  
pp. 1783-1790
Author(s):  
Rawnaq KH. Ibraheem ◽  
Abdulrahman H. Majeed
Keyword(s):  
Jordan Homomorphism ◽  
Jordan Homomorphisms

     Let S be an inverse semiring, and U be an ideal of S. In this paper, we introduce   the concept of U-S Jordan homomorphism of inverse semirings, and extend the result  of  Herstein on Jordan homomorphisms in inverse semirings.

Extending Jordan Ideals and Jordan Homomorphisms of Symmetric Elements in a Ring with Involution

1972 ◽  
Vol 24 (1) ◽  
pp. 50-59 ◽  
Author(s):  
Kirby C. Smith
Keyword(s):  
Associative Ring ◽  
Background Information ◽  
Matrix Rings ◽  
Jordan Ring ◽  
Jordan Homomorphism ◽  
Rings With Involution ◽  
Jordan Homomorphisms ◽  
Definition Of ◽  
Natural Way

In this work, we show how the ideas in [3, pp. 6-12] can be used to give conditions under which Jordan ideals in the set of symmetric elements in an associative ring R with involution extend to associative ideals of R in a natural way. We also give conditions under which a Jordan homomorphism of the set of symmetric elements will extend to an associative homomorphism of R. Such work has been done on matrix rings with involution in [5; 6]. An abstract definition of a Jordan ring may be found in [3] as well as other background information.

scholarly journals Nearly Jordan -Homomorphisms between Unital -Algebras

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
A. Ebadian ◽  
S. Kaboli Gharetapeh ◽  
M. Eshaghi Gordji
Keyword(s):  
Fixed Points ◽  
Continuous Mapping ◽  
Linear Mapping ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
Unital Algebra ◽  
Jordan Homomorphism ◽  
Jordan Homomorphisms ◽  
Rassias Stability

Let , be two unital -algebras. We prove that every almost unital almost linear mapping : which satisfies for all , all , and all , is a Jordan homomorphism. Also, for a unital -algebra of real rank zero, every almost unital almost linear continuous mapping is a Jordan homomorphism when holds for all (), all , and all . Furthermore, we investigate the Hyers- Ulam-Aoki-Rassias stability of Jordan -homomorphisms between unital -algebras by using the fixed points methods.

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