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Some inequalities for unitarily invariant norms of matrices [PDF]

Journal of Inequalities and Applications, 2011
This article aims to discuss inequalities involving unitarily invariant norms. We obtain a refinement of the inequality shown by Zhan. Meanwhile, we give an improvement of the inequality presented by Bhatia and Kittaneh for the Hilbert-Schmidt norm ...
Wang Shaoheng, Zou Limin, Jiang Youyi
doaj   +8 more sources

Unitarily invariant norm inequalities for operators

Journal of the Egyptian Mathematical Society, 2012
10 pages, Accepted ...
Mohsen Erfanian Omidvar, Mohammad Sal Moslehian, ‎A‎. ‎Niknam‎   +2 more
core   +4 more sources

Unitarily invariant norm inequalities for matrix means [PDF]

Journal of Analysis, 2021
AbstractThe main target of this article is to present several unitarily invariant norm inequalities which are refinements of arithmetic-geometric mean, Heinz and Cauchy-Schwartz inequalities by convexity of some special functions.
Hongliang Zuo
exaly   +4 more sources

New proofs on two recent inequalities for unitarily invariant norms [PDF]

Journal of Inequalities and Applications, 2020
In this short note, we provide alternative proofs for several recent results due to Audenaert (Oper. Matrices 9:475–479, 2015) and Zou (J. Math. Inequal. 10:1119–1122, 2016; Linear Algebra Appl. 552:154–162, 2019).
Junjian Yang, Linzhang Lu
doaj   +2 more sources

Unitarily invariant Norms on Operators [PDF]

Acta Scientiarum Mathematicarum, 2021
Let $f$ be a symmetric norm on ${\mathbb R}^n$ and let ${\mathcal B}({\mathcal H})$ be the set of all bounded linear operators on a Hilbert space ${\mathcal H}$ of dimension at least $n$. Define a norm on ${\mathcal B}({\mathcal H})$ by $\|A\|_f = f(s_1(A), \dots, s_n(A))$, where $s_k(A) = \inf\{\|A-X\|: X\in {\mathcal B}({\mathcal H}) \hbox{ has rank ...
Jor-Ting Chan, Chi-Kwong Li
openalex   +3 more sources

Norm inequalities for functions of matrices [PDF]

Heliyon
In this paper, we prove several spectral norm and unitarily invariant norm inequalities for matrices in which the special cases of our results present some known inequalities. Also, some of our results give interpolating inequalities which are related to
Ahmad Al-Natoor
doaj   +2 more sources

Quadratic Forms in Random Matrices with Applications in Spectrum Sensing [PDF]

Entropy
Quadratic forms with random kernel matrices are ubiquitous in applications of multivariate statistics, ranging from signal processing to time series analysis, biomedical systems design, wireless communications performance analysis, and other fields ...
Daniel Gaetano Riviello, Giusi Alfano, Roberto Garello   +2 more
doaj   +2 more sources

A class of unitarily invariant norms on 𝐵(𝐻) [PDF]

Proceedings of the American Mathematical Society, 2000
Let H H be a complex Hilbert space and let
Jor-Ting Chan, Chi-Kwong Li, Charlies Tu
openalex   +3 more sources

Unitarily invariant norms on dual quaternion matrices

Pacific Journal of Optimization, 2023
Summary: Dual quaternion matrices have recently received significant attention in research. In this paper, we primarily investigate unitarily invariant norms of dual quaternion matrices. We first introduce symmetric gauge function on dual numbers and establish a one-to-one correspondence between unitarily invariant norms of dual quaternion matrices and
Sheng Chen, Hu Haofei
openalex   +3 more sources

Some inequalities for unitarily invariant norms [PDF]

Operators and Matrices, 2014
In this note, we use the convexity of the function φ(v) to sharpen the matrix version of the Heinz means, where φ(v) is defined as φ(v) = ‖AvXB1−v + A1−vXBv‖ on [0,1] for A,B,X ∈ Mn such that A and B are positive semidefinite, and also give a refinement of the inequality [Theorem 6, SIAM J. Matrix Anal. Appl.
Junliang Wu, Jianguo Zhao
openalex   +2 more sources