Nonlinear maps commuting with the λ-Aluthge transform under (n,m)–Jordan-triple product

2018 ◽  
Vol 67 (12) ◽  
pp. 2382-2398
Author(s):  
Fadil Chabbabi ◽  
Mostafa Mbekhta
Keyword(s):  
Triple Product ◽  
Aluthge Transform ◽  
Nonlinear Maps ◽  
Jordan Triple Product

scholarly journals Zero Triple Product Determined Matrix Algebras

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Hongmei Yao ◽  
Baodong Zheng
Keyword(s):  
Linear Operator ◽  
Matrix Algebra ◽  
Triple Product ◽  
Unital Algebra ◽  
Matrix Algebras ◽  
Unital Ring ◽  
Jordan Triple Product

LetAbe an algebra over a commutative unital ringC. We say thatAis zero triple product determined if for everyC-moduleXand every trilinear map{⋅,⋅,⋅}, the following holds: if{x,y,z}=0wheneverxyz=0, then there exists aC-linear operatorT:A3⟶Xsuch thatx,y,z=T(xyz)for allx,y,z∈A. If the ordinary triple product in the aforementioned definition is replaced by Jordan triple product, thenAis called zero Jordan triple product determined. This paper mainly shows that matrix algebraMn(B),n≥3, whereBis any commutative unital algebra even different from the above mentioned commutative unital algebraC, is always zero triple product determined, andMn(F),n≥3, whereFis any field with chF≠2, is also zero Jordan triple product determined.

scholarly journals Nonlinear maps preserving condition spectrum of Jordan skew triple product of operators

2018 ◽  
pp. 933-942
Author(s):  
H. Benbouziane ◽  
Y. Bouramdane ◽  
M. Ech-Cherif El Kettani ◽  
A. Lahssaini
Keyword(s):  
Triple Product ◽  
Nonlinear Maps

Jordan Triple Product Homomorphisms on Triangular Matrices to and from Dimension One

2018 ◽  
Vol 33 ◽  
pp. 147-159
Author(s):  
Damjana Kokol Bukovsek ◽  
Blaz Mojskerc
Keyword(s):  
Triple Product ◽  
Complex Numbers ◽  
Triangular Matrices ◽  
Upper Triangular Matrices ◽  
Continuous Maps ◽  
Dimension One ◽  
Jordan Triple Product

A map $\Phi$ is a Jordan triple product (JTP for short) homomorphism whenever $\Phi(A B A)= \Phi(A) \Phi(B) \Phi(A)$ for all $A,B$. We study JTP homomorphisms on the set of upper triangular matrices $\mathcal{T}_n(\mathbb{F})$, where $\Ff$ is the field of real or complex numbers. We characterize JTP homomorphisms $\Phi: \mathcal{T}_n(\mathbb{C}) \to \mathbb{C}$ and JTP homomorphisms $\Phi: \mathbb{F} \to \mathcal{T}_n(\mathbb{F})$. In the latter case we consider continuous maps and the implications of omitting the assumption of continuity.

Maps preserving Jordan triple product on the self-adjoint elements of C∗-algebras

2016 ◽  
Vol 10 (02) ◽  
pp. 1750022 ◽  
Author(s):  
Ali Taghavi
Keyword(s):  
Triple Product ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
Absolute Value ◽  
C Algebras ◽  
Complex Linear ◽  
Jordan Homomorphisms ◽  
Jordan Triple Product ◽  
Unit Formula

Let [Formula: see text] and [Formula: see text] be two unital [Formula: see text]-algebras with unit [Formula: see text]. It is shown that the mapping [Formula: see text] which preserves arithmetic mean and Jordan triple product is a difference of two Jordan homomorphisms provided that [Formula: see text]. The structure of [Formula: see text] is more refined when [Formula: see text] or [Formula: see text]. Furthermore, if [Formula: see text] is a [Formula: see text]-algebra of real rank zero and [Formula: see text] is additive and preserves absolute value of product, then [Formula: see text] such that [Formula: see text] (respectively, [Formula: see text]) is a complex linear (respectively, antilinear) ∗-homomorphism.

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