scholarly journals Multiplicative perturbation bounds of the group inverse and oblique projection

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3171-3175 ◽  
Author(s):  
Lingsheng Meng ◽  
Bing Zheng
Keyword(s):  
Unitarily Invariant Norm ◽  
Group Inverse ◽  
Oblique Projection ◽  
Perturbation Bounds ◽  
Invariant Norm ◽  
Multiplicative Perturbation

In this paper, the multiplicative perturbation bounds of the group inverse and related oblique projection under general unitarily invariant norm are presented by using the decompositions of B# - A# and BB# - AA#.

Norm inequalities for positive semi-definite matrices and a question of Bourin II

2021 ◽  
pp. 2150043
Author(s):  
Mostafa Hayajneh ◽  
Saja Hayajneh ◽  
Fuad Kittaneh
Keyword(s):  
Affirmative Answer ◽  
Unitarily Invariant Norm ◽  
Norm Inequalities ◽  
Invariant Norm ◽  
Special Case

Let [Formula: see text] and [Formula: see text] be [Formula: see text] positive semi-definite matrices. It is shown that [Formula: see text] for every unitarily invariant norm. This gives an affirmative answer to a question of Bourin in a special case. It is also shown that [Formula: see text] for [Formula: see text] and for every unitarily invariant norm.

scholarly journals Some Hermite-Hadamard type integral inequalities for operator AG-preinvex functions

2016 ◽  
Vol 8 (2) ◽  
pp. 312-323
Author(s):  
Ali Taghavi ◽  
Haji Mohammad Nazari ◽  
Vahid Darvish
Keyword(s):  
Integral Inequalities ◽  
Unitarily Invariant Norm ◽  
Norm Inequalities ◽  
Invariant Norm ◽  
Type Integral ◽  
Preinvex Functions ◽  
Inequalities For Operators

Abstract In this paper, we introduce the concept of operator AG-preinvex functions and prove some Hermite-Hadamard type inequalities for these functions. As application, we obtain some unitarily invariant norm inequalities for operators.

Improved Young and Heinz operator inequalities for unitarily invariant norms

2020 ◽  
Vol 70 (2) ◽  
pp. 453-466
Author(s):  
A. Beiranvand ◽  
Amir Ghasem Ghazanfari
Keyword(s):  
Hilbert Space ◽  
Type Inequality ◽  
Young Inequality ◽  
Unitarily Invariant Norm ◽  
Operator Inequalities ◽  
Schmidt Norm ◽  
Unitarily Invariant Norms ◽  
Invariant Norm ◽  
Kantorovich Constant ◽  
New Inequalities

Abstract In this paper, we present numerous refinements of the Young inequality by the Kantorovich constant. We use these improved inequalities to establish corresponding operator inequalities on a Hilbert space and some new inequalities involving the Hilbert-Schmidt norm of matrices. We also give some refinements of the following Heron type inequality for unitarily invariant norm |||⋅||| and A, B, X ∈ Mn(ℂ): $$\begin{array}{} \begin{split} \displaystyle \Big|\Big|\Big|\frac{A^\nu XB^{1-\nu}+A^{1-\nu}XB^\nu}{2}\Big|\Big|\Big| \leq &(4r_0-1)|||A^{\frac{1}{2}}XB^{\frac{1}{2}}||| \\ &+2(1-2r_0)\Big|\Big|\Big|(1-\alpha)A^{\frac{1}{2}}XB^{\frac{1}{2}} +\alpha\Big(\frac{AX+XB}{2}\Big)\Big|\Big|\Big|, \end{split} \end{array}$$ where $\begin{array}{} \displaystyle \frac{1}{4}\leq \nu \leq \frac{3}{4}, \alpha \in [\frac{1}{2},\infty ) \end{array}$ and r0 = min{ν, 1 – ν}.

A certain generalization of the Heinz inequality for positive operators

2016 ◽  
Vol 27 (02) ◽  
pp. 1650008 ◽  
Author(s):  
Hideki Kosaki
Keyword(s):  
Positive Operators ◽  
Unitarily Invariant Norm ◽  
Heinz Inequality ◽  
Norm Inequalities ◽  
Invariant Norm

Norm inequalities of the form [Formula: see text] with [Formula: see text] and [Formula: see text] are studied. Here, [Formula: see text] are operators with [Formula: see text] and [Formula: see text] is an arbitrary unitarily invariant norm. We show that the inequality holds true if and only if [Formula: see text].

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