Arithmetic–Geometric Mean and Related Submajorisation and Norm Inequalities for $$\tau $$-Measurable operators: Part I

2020 ◽  
Vol 92 (3) ◽  
Author(s):  
P. G. Dodds ◽  
T. K. Dodds ◽  
F. A. Sukochev ◽  
D. Zanin
Keyword(s):  
Geometric Mean ◽  
Norm Inequalities ◽  
Measurable Operators

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 Inequalities for sector matrices and positive linear maps

2019 ◽  
Vol 35 ◽  
pp. 418-423 ◽  
Author(s):  
Fuping Tan ◽  
Huimin Che
Keyword(s):  
Geometric Mean ◽  
Positive Definite ◽  
Norm Inequalities ◽  
Linear Map ◽  
Linear Maps ◽  
Positive Linear Map ◽  
Positive Linear Maps

Ando proved that if A, B are positive definite, then for any positive linear map Φ, it holds Φ(A#λB) ≤ Φ(A)#λΦ(B), where A#λB, 0 ≤ λ ≤ 1, means the weighted geometric mean of A, B. Using the recently defined geometric mean for accretive matrices, Ando’s result is extended to sector matrices. Some norm inequalities are considered as well.    

scholarly journals Norm inequalities related to the matrix geometric mean

2012 ◽  
Vol 437 (2) ◽  
pp. 726-733 ◽  
Author(s):  
Rajendra Bhatia ◽  
Priyanka Grover
Keyword(s):  
Geometric Mean ◽  
Norm Inequalities ◽  
The Matrix

scholarly journals Extensions of recent combinatorial refinements of discrete and integral Jensen inequalities

2021 ◽  
Author(s):  
László Horváth
Keyword(s):  
Information Theory ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Jensen Inequality ◽  
Arithmetic Means ◽  
Norm Inequalities ◽  
Integrable Functions ◽  
Essential Extensions ◽  
Vector Valued

AbstractThe main purpose of this work is to present essential extensions of results in [7] and [8], and apply them to some special situations. Of particular interest is the refinement of the integral Jensen inequality for vector valued integrable functions. The applications related to four topics, namely f-divergences in information theory (an interesting refinement of the weighted geometric mean–arithmetic mean inequality is obtained as a consequence), norm inequalities, quasi-arithmetic means, Hölder’s and Minkowski’s inequalities.

scholarly journals A new generalization of refined young inequalities for τ-measurable operators

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1253-1265
Author(s):  
Mohamed Ighachane ◽  
Mohamed Akkouchi
Keyword(s):  
Geometric Mean ◽  
Measurable Operators

In this paper, by the arithmetic-geometric mean inequality, we give a new generalization of refined Young?s inequality. As applications we present some new generalizations of refinements of Young inequalities for the determinants, traces and p-norms of ?-measurable operators.

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