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.

Norm inequalities for positive semidefinite matrices and a question of Bourin

2017 ◽  
Vol 28 (14) ◽  
pp. 1750102 ◽  
Author(s):  
Mostafa Hayajneh ◽  
Saja Hayajneh ◽  
Fuad Kittaneh
Keyword(s):  
Positive Semidefinite ◽  
Affirmative Answer ◽  
Unitarily Invariant Norm ◽  
Trace Norm ◽  
Positive Semidefinite Matrices ◽  
Norm Inequalities ◽  
Invariant Norm

Let [Formula: see text] such that [Formula: see text] and [Formula: see text] are positive semidefinite. It is shown that [Formula: see text] for [Formula: see text] and for every unitarily invariant norm. This gives an affirmative answer to one of the questions posed by Bourin regarding subadditivity inequalities in the case of the trace norm. New norm inequalities related to Bourin's question are also presented.

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).

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