Singular value and unitarily invariant norm inequalities for sums and products of operators

2021 ◽  
Vol 6 (4) ◽  
Author(s):  
Jianguo Zhao
Keyword(s):  
Singular Value ◽  
Unitarily Invariant Norm ◽  
Norm Inequalities ◽  
Invariant Norm

scholarly journals Singular value inequalities for sector matrices

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5231-5236
Author(s):  
Jianming Xue ◽  
Xingkai Hu
Keyword(s):  
Singular Value ◽  
Unitarily Invariant Norm ◽  
Norm Inequalities ◽  
Invariant Norm

In this paper, we present two singular value inequalities for sector matrices. As a consequence, we prove unitarily invariant norm inequalities for sector matrices. Moreover, we present some determinant inequalities for accretive-dissipative matrices.

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.

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].

Some Norm Inequalities for Operators

1999 ◽  
Vol 42 (1) ◽  
pp. 87-96 ◽  
Author(s):  
Fuad Kittaneh
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Geometric Mean ◽  
Continuous Functions ◽  
Unitarily Invariant Norm ◽  
Norm Inequalities ◽  
Invariant Norm ◽  
Inequalities For Operators

AbstractLet Ai , Bi and Xi (i = 1, 2,…,n) be operators on a separable Hilbert space. It is shown that if f and g are nonnegative continuous functions on [0, ∞) which satisfy the relation f(t)g(t) = t for all t in [0, ∞), thenfor every r > 0 and for every unitarily invariant norm. This result improves some known Cauchy-Schwarz type inequalities. Norm inequalities related to the arithmetic-geometric mean inequality and the classical Heinz inequalities are also obtained.

scholarly journals Norm inequalities for submultiplicative functions involving contraction sector $2 \times 2$ block matrices

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaoying Zhou
Keyword(s):  
Unitarily Invariant Norm ◽  
Norm Inequalities ◽  
Block Matrices ◽  
Link Type ◽  
Invariant Norm

AbstractIn this article, we show unitarily invariant norm inequalities for sector $2\times 2$ 2 × 2 block matrices which extend and refine some recent results of Bourahli, Hirzallah, and Kittaneh (Positivity, 2020, 10.1007/s11117-020-00770-w).

Sign in / Sign up

Export Citation Format

Share Document