Norm inequalities for fractional powers of positive operators

1993 ◽  
Vol 27 (4) ◽  
pp. 279-285 ◽  
Author(s):  
Fuad Kittaneh
Keyword(s):  
Positive Operators ◽  
Fractional Powers ◽  
Norm Inequalities

scholarly journals NORM AND ANTI-NORM INEQUALITIES FOR POSITIVE SEMI-DEFINITE MATRICES

2011 ◽  
Vol 22 (08) ◽  
pp. 1121-1138 ◽  
Author(s):  
JEAN-CHRISTOPHE BOURIN ◽  
FUMIO HIAI
Keyword(s):  
Positive Operators ◽  
Norm Inequalities ◽  
Block Matrices ◽  
Determinantal Inequality ◽  
Unitarily Invariant Norms ◽  
Analytic Criterion

Some subadditivity results involving symmetric (unitarily invariant) norms are obtained. For instance, if [Formula: see text] is a polynomial of degree m with non-negative coefficients, then, for all positive operators A, B and all symmetric norms, [Formula: see text] To give parallel superadditivity results, we investigate anti-norms, a class of functionals containing the Schatten q-norms for q ∈ (0, 1] and q < 0. The results are extensions of the Minkowski determinantal inequality. A few estimates for block-matrices are derived. For instance, let f : [0, ∞) → [0, ∞) be concave and p ∈(1, ∞). If fp(t) is superadditive, then [Formula: see text] for all positive m × m matrix A = [aij]. Furthermore, for the normalized trace τ, we consider functions φ(t) and f(t) for which the functional A ↦ φ ◦ τ ◦ f(A) is convex or concave, and obtain a simple analytic criterion.

A note on fractional powers of strongly positive operators and their applications

2019 ◽  
Vol 22 (2) ◽  
pp. 302-325 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Ayman Hamad
Keyword(s):  
Banach Space ◽  
Elliptic Operators ◽  
Positive Operators ◽  
Fractional Powers ◽  
Fractional Spaces

Abstract The present paper deals with fractional powers of positive operators in a Banach space. The main theorem concerns the structure of fractional powers of positive operators in fractional spaces. As applications, the structure of fractional powers of elliptic operators is studied.

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].

Norm Inequalities for Sums of Positive Operators. II

Positivity ◽  
2006 ◽  
Vol 10 (2) ◽  
pp. 251-260 ◽  
Author(s):  
Fuad Kittaneh
Keyword(s):  
Positive Operators ◽  
Norm Inequalities
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