Perturbation bounds for weighted polar decomposition in the weighted unitarily invariant norm

2008 ◽  
Vol 15 (8) ◽  
pp. 685-700 ◽  
Author(s):  
Hu Yang ◽  
Hanyu Li
Keyword(s):  
Polar Decomposition ◽  
Unitarily Invariant Norm ◽  
Perturbation Bounds ◽  
Invariant Norm

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}.

scholarly journals Relative and Absolute Perturbation Bounds for Weighted Polar Decomposition

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Pingping Zhang ◽  
Hu Yang ◽  
Hanyu Li
Keyword(s):  
Polar Decomposition ◽  
Perturbation Bounds ◽  
New Perturbation

Some new perturbation bounds for both weighted unitary polar factors and generalized nonnegative polar factors of the weighted polar decompositions are presented without the restriction thatAand its perturbed matrixA˜have the same rank. These bounds improve the corresponding recent results.

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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