scholarly journals Lie higher derivations on triangular algebras revisited

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3187-3194 ◽  
Author(s):  
F. Moafian ◽  
Ebrahimi Vishki
Keyword(s):  
Direct Proof ◽  
Acta Math ◽  
Multilinear Algebra ◽  
Triangular Algebra ◽  
Higher Derivation ◽  
Linear Multilinear Algebra ◽  
Triangular Algebras

Motivated by the extensive works of W.-S. Cheung [Linear Multilinear Algebra, 51 (2003), 299-310] and X.F. Qi [Acta Math. Sinica, English Series, 29 (2013), 1007-1018], we present the structure of Lie higher derivations on a triangular algebra explicitly. We then study those conditions under which a Lie higher derivation on a triangular algebra is proper. Our approach provides a direct proof for some known results concerning to the properness of Lie higher derivations on triangular algebras.

scholarly journals Generalized Higher Derivations on Lie Ideals of Triangular Algebras

2017 ◽  
Vol 25 (1) ◽  
pp. 35-53
Author(s):  
Mohammad Ashraf ◽  
Nazia Parveen ◽  
Bilal Ahmad Wani
Keyword(s):  
Commutative Ring ◽  
Lie Ideal ◽  
Additive Subgroup ◽  
Triangular Algebra ◽  
Higher Derivation ◽  
Square Closed Lie Ideal ◽  
Triangular Algebras

Abstract Let be the triangular algebra consisting of unital algebras A and B over a commutative ring R with identity 1 and M be a unital (A; B)-bimodule. An additive subgroup L of A is said to be a Lie ideal of A if [L;A] ⊆ L. A non-central square closed Lie ideal L of A is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on A, every generalized Jordan triple higher derivation of L into A is a generalized higher derivation of L into A.

scholarly journals Generalized Jordan triple (σ,τ)-higher derivation on triangular algebras

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2285-2294
Author(s):  
Mohammad Ashraf ◽  
Aisha Jabeen ◽  
Mohd Akhtar
Keyword(s):  
Commutative Ring ◽  
Triangular Algebra ◽  
Higher Derivation ◽  
Triangular Algebras

Let R be a commutative ring with unity, U = Tri(A,M,B) be a triangular algebra consisting of unital algebras A,B and (A,B)-bimodule M which is faithful as a left A-module and also as a right B-module. Let ? and ? be two automorphisms of U. A family ? = {?n}n?N of R-linear mappings ?n : U ? U is said to be a generalized Jordan triple (?,?)-higher derivation on A if there exists a Jordan triple (?,?)-higher derivation D = {dn}n?N on U such that ?0 = IU, the identity map of U and ?n(XYX) = ?i+j+k=n ?i(?n-i(X))dj(?k?i(Y))dk(?n-k(X)) holds for all X,Y ? U and each n ? N. In this article, we study generalized Jordan triple (?,?)-higher derivation on A and prove that every generalized Jordan triple (?,?)-higher derivation on U is a generalized (?,?)-higher derivation on U.

scholarly journals Zero-Sum Coefficient Derivations in Three Variables of Triangular Algebras

2016 ◽  
Vol 8 (5) ◽  
pp. 37
Author(s):  
Youngsoo Kim ◽  
Byunghoon Lee
Keyword(s):  
Standard Form ◽  
Sufficient Conditions ◽  
Multilinear Polynomial ◽  
Triangular Algebra ◽  
Triangular Algebras ◽  
Zero Sum ◽  
Lie Derivations

Under mild assumptions Benkovi\v{c} showed that an $f$-derivation of a triangular algebra is a derivation when the sum of the coefficients of the multilinear polynomial $f$ is nonzero. We investigate the structure of $f$-derivations of triangular algebras when $f$ is of degree 3 and the coefficient sum is zero. The zero-sum coeffient derivations include Lie derivations (degree 2) and Lie triple derivations (degree 3), which have been previously shown to be not necessarily derivations but in standard form, i.e., the sum of a derivation and a central map. In this paper, we present sufficient conditions on the coefficients of $f$ to ensure that any $f$-derivations are derivations or are in standard form.<br /><br />

scholarly journals New Refinement of the Operator Kantorovich Inequality

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 139
Author(s):  
Hamid Moradi ◽  
Shigeru Furuichi ◽  
Zahra Heydarbeygi
Keyword(s):  
Multilinear Algebra ◽  
Kantorovich Inequality ◽  
Linear Multilinear Algebra

We focus on the improvement of operator Kantorovich type inequalities. Among the consequences, we improve the main result of the paper [H.R. Moradi, I.H. Gümüş, Z. Heydarbeygi, A glimpse at the operator Kantorovich inequality, Linear Multilinear Algebra, doi:10.1080/03081087.2018.1441799].

Superalgebras with superinvolution or graded involution with colengths sequence bounded by 3

2020 ◽  
Vol 30 (04) ◽  
pp. 821-838
Author(s):  
Antonio Ioppolo
Keyword(s):  
Characteristic Zero ◽  
Analogous Result ◽  
Multilinear Algebra ◽  
Finite Dimensional ◽  
Linear Multilinear Algebra

Let [Formula: see text] be a superalgebra with superinvolution or graded involution over a field of characteristic zero and let [Formula: see text], [Formula: see text], be the [Formula: see text]-cocharacter of [Formula: see text]. The ∗-colengths sequence, [Formula: see text], [Formula: see text], is the sum of the multiplicities in the decomposition of the [Formula: see text]-cocharacter [Formula: see text], for all [Formula: see text]. The main purpose of this paper is to classify the superalgebras with superinvolution with ∗-colengths sequence bounded by three. Moreover, we shall extend to the general case, the analogous result proved by do Nascimento and Vieira in [Superalgebras with graded involution and star-graded colength bounded by 3, Linear Multilinear Algebra 67(10) (2019) 1999–2020] for finite-dimensional superalgebras with graded involution.

scholarly journals On weighted means and their inequalities

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mustapha Raïssouli ◽  
Shigeru Furuichi
Keyword(s):  
Multilinear Algebra ◽  
Monotone Functions ◽  
Weighted Arithmetic ◽  
Related Operator ◽  
Weighted Means ◽  
Operator Version ◽  
Linear Multilinear Algebra ◽  
Operator Monotone Functions ◽  
Harmonic Means ◽  
Stabilizable Means

AbstractIn (Pal et al. in Linear Multilinear Algebra 64(12):2463–2473, 2016), Pal et al. introduced some weighted means and gave some related inequalities by using an approach for operator monotone functions. This paper discusses the construction of these weighted means in a simple and nice setting that immediately leads to the inequalities established there. The related operator version is here immediately deduced as well. According to our constructions of the means, we study all cases of the weighted means from three weighted arithmetic/geometric/harmonic means by the use of the concept such as stable and stabilizable means. Finally, the power symmetric means are studied and new weighted power means are given.

Nonlinear Lie triple derivations by local actions on triangular algebras

2021 ◽  
Author(s):  
Xingpeng Zhao
Keyword(s):  
Commutative Ring ◽  
Triangular Algebra ◽  
Mild Conditions ◽  
Derivation Formula ◽  
Triangular Algebras

Let [Formula: see text] be a triangular algebra over a commutative ring [Formula: see text]. In this paper, under some mild conditions on [Formula: see text], we prove that if [Formula: see text] is a nonlinear map satisfying [Formula: see text] for any [Formula: see text] with [Formula: see text]. Then [Formula: see text] is almost additive on [Formula: see text], that is, [Formula: see text] Moreover, there exist an additive derivation [Formula: see text] of [Formula: see text] and a nonlinear map [Formula: see text] such that [Formula: see text] for [Formula: see text], where [Formula: see text] for any [Formula: see text] with [Formula: see text].

A note on non-linear ∗-Jordan derivations on ∗-algebras

2019 ◽  
Vol 69 (3) ◽  
pp. 639-646
Author(s):  
Ali Taghavi ◽  
Mojtaba Nouri ◽  
Mehran Razeghi ◽  
Vahid Darvish
Keyword(s):  
Von Neumann Algebras ◽  
Short Note ◽  
Multilinear Algebra ◽  
Von Neumann ◽  
Non Linear ◽  
Linear Multilinear Algebra

Abstract Taghavi et al. in [TAGHAVI, A.—ROHI, H.—DARVISH, V.: Non-linear ∗-Jordan derivations on von Neumann algebras, Linear Multilinear Algebra 64 (2016), 426–439] proved that the map Φ: 𝓐 → 𝓐 which satisfies the following condition $$\begin{array}{} \Phi(A\diamond B)=\Phi(A)\diamond B+A\diamond \Phi(B) \end{array} $$ where A ⋄ B = AB+BA* for every A, B ∈ 𝓐 is an additive ∗-derivation. In this short note, we prove that when A is a prime ∗-algebras and Φ: 𝓐 → 𝓐 satisfies the above condition, then Φ is ∗-additive. Moreover, if Φ(iI) is self-adjoint then Φ is derivation.

scholarly journals The Characterization of Generalized Jordan Centralizers on Triangular Algebras

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Quanyuan Chen ◽  
Xiaochun Fang ◽  
Changjing Li
Keyword(s):  
Triangular Algebra ◽  
Additive Operator ◽  
Triangular Algebras

In this paper, it is shown that if T=Tri(A,M,B) is a triangular algebra and ϕ is an additive operator on T such that (m+n+k+l)ϕ(T2)-(mϕ(T)T+nTϕ(T)+kϕ(I)T2+lT2ϕ(I))∈FI for any T∈T, then ϕ is a centralizer. It follows that an (m,n)- Jordan centralizer on a triangular algebra is a centralizer.

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