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.

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 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.

Classification of involutions on finitary incidence algebras

2014 ◽  
Vol 24 (08) ◽  
pp. 1085-1098 ◽  
Author(s):  
Rosali Brusamarello ◽  
Érica Zancanella Fornaroli ◽  
Ednei Aparecido Santulo
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Sufficient Conditions ◽  
Decomposition Theorem ◽  
Multilinear Algebra ◽  
Partially Ordered ◽  
Incidence Algebras ◽  
Linear Multilinear Algebra ◽  
Necessary And Sufficient

Let X be a connected partially ordered set and let K be a field of characteristic different from 2. We present necessary and sufficient conditions for two involutions on the finitary incidence algebra of X over K, FI (X), to be equivalent in the case when every multiplicative automorphism of FI (X) is inner. To get the classification of involutions we extend the concept of multiplicative automorphism to finitary incidence algebras and prove the Decomposition Theorem of involutions of [Anti-automorphisms and involutions on (finitary) incidence algebras, Linear Multilinear Algebra 60 (2012) 181–188] for finitary incidence algebras.

scholarly journals Some improvements on the Ky Fan theorem for tensors

2021 ◽  
Vol 40 (2) ◽  
Author(s):  
Mohsen Tourang ◽  
Mostafa Zangiabadi
Keyword(s):  
Multilinear Algebra ◽  
Numerical Examples ◽  
Eigenvalue Localization ◽  
Fan Theorem ◽  
Linear Multilinear Algebra ◽  
Numer Math ◽  
Ky Fan ◽  
Localization Sets ◽  
Ky Fan Theorem ◽  
Perron Vector

AbstractThe improvements of Ky Fan theorem are given for tensors. First, based on Brauer-type eigenvalue inclusion sets, we obtain some new Ky Fan-type theorems for tensors. Second, by characterizing the ratio of the smallest and largest values of a Perron vector, we improve the existing results. Third, some new eigenvalue localization sets for tensors are given and proved to be tighter than those presented by Li and Ng (Numer Math 130(2):315–335, 2015) and Wang et al. (Linear Multilinear Algebra 68(9):1817–1834, 2020). Finally, numerical examples are given to validate the efficiency of our new bounds.

Factor rank preservers of matrices over additively-idempotent multiplicatively-cancellative semirings

2020 ◽  
pp. 2150072
Author(s):  
Sushobhan Maity ◽  
A. K. Bhuniya
Keyword(s):  
Boolean Algebra ◽  
Linear Algebra ◽  
Linear Operators ◽  
Multilinear Algebra ◽  
Boolean Rank ◽  
Max Algebra ◽  
Linear Multilinear Algebra

Here, we characterize the linear operators that preserve factor rank of matrices over additively-idempotent multiplicatively-cancellative semirings. The main results in this paper generalize the corresponding results on the two element Boolean algebra [L. B. Beasley and N. J. Pullman, Boolean-rank-preserving opeartors and Boolean-rank-1 spaces, Linear Algebra Appl. 59 (1984) 55–77] and on the max algebra [R. B. Bapat, S. Pati and S.-Z. Song, Rank preservers of matrices over max algebra, Linear Multilinear Algebra 48(2) (2000) 149–164]; and hold on max-plus algebra and some other tropical semirings.

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