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.

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 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 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.

ORTHOGONALITY PRESERVERS REVISITED

2009 ◽  
Vol 02 (03) ◽  
pp. 387-405 ◽  
Author(s):  
María Burgos ◽  
Francisco J. Fernández-Polo ◽  
Jorge J. Garcés ◽  
Antonio M. Peralta
Keyword(s):  
Linear Operator ◽  
Natural Product ◽  
Bounded Linear Operator ◽  
Complete Characterization ◽  
Bounded Linear ◽  
C Algebra ◽  
Jordan Homomorphism ◽  
C Algebras ◽  
Orthogonality Preservers

We obtain a complete characterization of all orthogonality preserving operators from a JB *-algebra to a JB *-triple. If T : J → E is a bounded linear operator from a JB *-algebra (respectively, a C *-algebra) to a JB *-triple and h denotes the element T**(1), then T is orthogonality preserving, if and only if, T preserves zero-triple-products, if and only if, there exists a Jordan *-homomorphism [Formula: see text] such that S(x) and h operator commute and T(x) = h•r(h) S(x), for every x ∈ J, where r(h) is the range tripotent of h, [Formula: see text] is the Peirce-2 subspace associated to r(h) and •r(h) is the natural product making [Formula: see text] a JB *-algebra. This characterization culminates the description of all orthogonality preserving operators between C *-algebras and JB *-algebras and generalizes all the previously known results in this line of study.

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.

Characterizations of linear mappings through zero products or zero Jordan products

2016 ◽  
Vol 31 ◽  
pp. 408-424 ◽  
Author(s):  
Guangyu An ◽  
Jiankui Li
Keyword(s):  
Linear Mapping ◽  
Generalized Derivations ◽  
Jordan Product ◽  
Unital Algebra ◽  
Left Derivation ◽  
Jordan Homomorphisms ◽  
Jordan Products ◽  
Lie Derivations

Let $\mathcal{A}$ be a unital algebra and $\mathcal{M}$ be a unital $\mathcal{A}$-bimodule. A characterization of generalized derivations and generalized Jordan derivations from $\mathcal{A}$ into $\mathcal{M}$, through zero products or zero Jordan products, is given. Suppose that $\mathcal{M}$ is a unital left $\mathcal{A}$-module. It is investigated when a linear mapping from $\mathcal{A}$ into $\mathcal{M}$ is a Jordan left derivation under certain conditions. It is also studied whether an algebra with a nontrivial idempotent is zero Jordan product determined, and Jordan homomorphisms, Lie homomorphisms and Lie derivations on zero Jordan product determined algebras are characterized.

scholarly journals A Characterization of Jordan Homomorphism on Banach Algebras

2014 ◽  
Vol 2014 ◽  
pp. 1-3 ◽  
Author(s):  
Abbas Zivari-Kazempour
Keyword(s):  
Banach Algebras ◽  
Ring Homomorphism ◽  
Jordan Homomorphism

Let 𝒜 and ℬ be Banach algebras and let φ:𝒜→ℬ be a Jordan homomorphism. We show that, under special hypotheses, φ is ring homomorphism. Some related results 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.

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