Linear & multilinear algebra, ISSN 1563-5139, 2018, Volume 67, Issue 11, pp. 2253 - 2281

We present several Ando-Hiai type inequalities for n-variable operator means for positive invertible operators...

Ando-Hiai inequality | generalized Kantorovich constant | Karcher mean | power mean | geometric mean | Operator mean | Ando–Hiai inequality | MATRIX POWER | MATHEMATICS | Inequalities

Ando-Hiai inequality | generalized Kantorovich constant | Karcher mean | power mean | geometric mean | Operator mean | Ando–Hiai inequality | MATRIX POWER | MATHEMATICS | Inequalities

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 03/2018, Volume 540, pp. 234 - 243

Let α be in (0,1) and r>0 and #α stand for the weighted operator geometric mean. We consider the following statement:A,B>0,A#αB≥I⇒Ar#αBr≥I. Ando and Hiai show...

Operator monotone | Ando–Hiai inequality | Operator mean | MATHEMATICS | Ando-Hiai inequality | MATHEMATICS, APPLIED

Operator monotone | Ando–Hiai inequality | Operator mean | MATHEMATICS | Ando-Hiai inequality | MATHEMATICS, APPLIED

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 2008, Volume 429, Issue 7, pp. 1546 - 1554

In this paper, we present a complement of a generalized Ando–Hiai inequality due to Fujii and Kamei [M. Fujii, E. Kamei, Ando...

Generalized Kantorovich constant | Operator inequality | Araki–Cordes inequality | Ando–Hiai inequality | Positive operator | Operator mean | Ando-Hiai inequality | Araki-Cordes inequality | MATHEMATICS | Araki-Cordes | inequality | MATHEMATICS, APPLIED | generalized kantorovich constant | operator inequality | positive operator | operator mean | Equality

Generalized Kantorovich constant | Operator inequality | Araki–Cordes inequality | Ando–Hiai inequality | Positive operator | Operator mean | Ando-Hiai inequality | Araki-Cordes inequality | MATHEMATICS | Araki-Cordes | inequality | MATHEMATICS, APPLIED | generalized kantorovich constant | operator inequality | positive operator | operator mean | Equality

Journal Article

Annals of functional analysis, ISSN 2008-8752, 2010, Volume 1, Issue 2, pp. 28 - 45

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 10/2016, Volume 442, Issue 1, pp. 1 - 16

... the Cartan barycenter, is the canonical barycenter on Hadamard spaces. We establish an order inequality of probability measures on partially ordered symmetric spaces of non-compact type, namely symmetric cones...

Wasserstein geometry | Cartan barycenter | Hadamard space | Contractive barycenter | Ando–Hiai inequality | Symmetric cone | Ando-Hiai inequality | MATRIX POWER | MATHEMATICS, APPLIED | METRICS | SPACE | MATHEMATICS | OPTIMAL TRANSPORT | GEOMETRY | Equality

Wasserstein geometry | Cartan barycenter | Hadamard space | Contractive barycenter | Ando–Hiai inequality | Symmetric cone | Ando-Hiai inequality | MATRIX POWER | MATHEMATICS, APPLIED | METRICS | SPACE | MATHEMATICS | OPTIMAL TRANSPORT | GEOMETRY | Equality

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 03/2015, Volume 63, Issue 3, pp. 636 - 649

In this paper, from the viewpoint of the Ando-Hiai inequality, we make a comparison among three geometric means...

unitarily invariant norm | Specht ratio | matrix geometric mean | Kantorovich constant | Ando-Li-Mathias geometric mean | Ando-Hiai inequality | Karcher mean | chaotic geometric mean | Ando–Li–Mathias geometric mean | Ando–Hiai inequality | INEQUALITIES | 47A64 | 47A30 | 47A63 | MATHEMATICS | Inequality | Constants | Complement | Algebra | Chaos theory | Inequalities | Images

unitarily invariant norm | Specht ratio | matrix geometric mean | Kantorovich constant | Ando-Li-Mathias geometric mean | Ando-Hiai inequality | Karcher mean | chaotic geometric mean | Ando–Li–Mathias geometric mean | Ando–Hiai inequality | INEQUALITIES | 47A64 | 47A30 | 47A63 | MATHEMATICS | Inequality | Constants | Complement | Algebra | Chaos theory | Inequalities | Images

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 479, Issue 1, pp. 531 - 545

.... Next, we shall show two types of the Ando-Hiai inequalities for the solution of the generalized Karcher equation...

Relative operator entropy | Tsalise relative operator entropy | Karcher mean | The Ando-Hiai inequality | Generalized Karcher equation | Operator mean | MATRIX POWER | MATHEMATICS | MATHEMATICS, APPLIED | OPERATOR MEANS

Relative operator entropy | Tsalise relative operator entropy | Karcher mean | The Ando-Hiai inequality | Generalized Karcher equation | Operator mean | MATRIX POWER | MATHEMATICS | MATHEMATICS, APPLIED | OPERATOR MEANS

Journal Article

Mathematical inequalities & applications, ISSN 1331-4343, 01/2017, Volume 20, Issue 1, pp. 217 - 223

.... As an application, we give some reverses of Ando-Hiai and Golden-Thompson type inequalities. These new reverse inequalities, improve some known results.

Generalized Kantorovich constant | Golden-Thompson inequality | Unitarily invariant norm | Geometric mean | Ando-Hiai inequality | Reverse inequality | Doubly concave function | unitarily invariant norm | MATHEMATICS | MATRICES | generalized Kantorovich constant | reverse inequality | geometric mean

Generalized Kantorovich constant | Golden-Thompson inequality | Unitarily invariant norm | Geometric mean | Ando-Hiai inequality | Reverse inequality | Doubly concave function | unitarily invariant norm | MATHEMATICS | MATRICES | generalized Kantorovich constant | reverse inequality | geometric mean

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 09/2014, Volume 457, pp. 276 - 286

.... We investigate the following Furuta-type inequality: For some fixed continuous function h,A≥B>0⇒A−rσφrXh−r≤B(r≥1), where Xh is the positive solution of h...

Furuta inequality | Operator monotone | Ando–Hiai inequality | Operator mean | Ando-Hiai inequality | MATHEMATICS | MATHEMATICS, APPLIED | MAJORIZATION

Furuta inequality | Operator monotone | Ando–Hiai inequality | Operator mean | Ando-Hiai inequality | MATHEMATICS | MATHEMATICS, APPLIED | MAJORIZATION

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 01/2020, Volume 31, Issue 1, p. 2050007

We improve the existing Ando–Hiai inequalities for operator means and present new ones for operator perspectives in several ways...

MATRIX | Lie-Trotter formula | weak log-majorization | Ando-Hiai inequality | EXTENSION | MATHEMATICS | operator convex function | operator perspective | Log-Euclidean mean | operator monotone function | JENSEN | Operator mean | ENTROPY

MATRIX | Lie-Trotter formula | weak log-majorization | Ando-Hiai inequality | EXTENSION | MATHEMATICS | operator convex function | operator perspective | Log-Euclidean mean | operator monotone function | JENSEN | Operator mean | ENTROPY

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2014, Volume 413, Issue 1, pp. 422 - 429

Let f(t) be an operator monotone function. Then A⩽B implies f(A)⩽f(B), but the converse implication is not true. Let A♯B be the geometric mean of A,B⩾0. If...

Operator concave function | Geometric mean | Loewner–Heinz inequality | Operator monotone function | Karcher mean | Positive definite operators | Ando–Hiai inequality | Operator mean | Power mean | Ando-Hiai inequality | Loewner-Heinz inequality | MATRIX POWER | MATHEMATICS, APPLIED | MAJORIZATION | MONOTONE-FUNCTIONS | MATHEMATICS

Operator concave function | Geometric mean | Loewner–Heinz inequality | Operator monotone function | Karcher mean | Positive definite operators | Ando–Hiai inequality | Operator mean | Power mean | Ando-Hiai inequality | Loewner-Heinz inequality | MATRIX POWER | MATHEMATICS, APPLIED | MAJORIZATION | MONOTONE-FUNCTIONS | MATHEMATICS

Journal Article

12.
The Riemannian mean and matrix inequalities related to the Ando-Hiai inequality and chaotic order

Operators and Matrices, ISSN 1846-3886, 09/2012, Volume 6, Issue 3, pp. 577 - 588

.... In this paper, we derive the Ando-Hiai inequality for the Riemannian mean which is an extension of the well-known Ando-Hiai inequality of two-matrices...

The Riemannian manifold | Arithmetic-geometric mean inequality | Chaotic order | The Riemannian mean | The Ando-Hiai inequality | Operator inequality | Matrix inequality | Positive definite matrices | chaotic order | MATHEMATICS | operator inequality | the Ando-Hiai inequality | arithmetic-geometric mean inequality | the Riemannian manifold | the Riemannian mean | matrix inequality

The Riemannian manifold | Arithmetic-geometric mean inequality | Chaotic order | The Riemannian mean | The Ando-Hiai inequality | Operator inequality | Matrix inequality | Positive definite matrices | chaotic order | MATHEMATICS | operator inequality | the Ando-Hiai inequality | arithmetic-geometric mean inequality | the Riemannian manifold | the Riemannian mean | matrix inequality

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 03/2016, Volume 64, Issue 3, pp. 512 - 526

We obtain eigenvalue inequalities for matrix geometric means of positive definite matrices...

unitarily invariant norm | matrix geometric mean | Kantorovich constant | Secondary: 47A30 | Ando-Hiai inequality | Primary: 47A63 | Karcher mean | chaotic geometric mean | Ando–Hiai inequality | MATHEMATICS | Algebra | Inequalities | Norms | Eigenvalues | Constants | Complement | Invariants

unitarily invariant norm | matrix geometric mean | Kantorovich constant | Secondary: 47A30 | Ando-Hiai inequality | Primary: 47A63 | Karcher mean | chaotic geometric mean | Ando–Hiai inequality | MATHEMATICS | Algebra | Inequalities | Norms | Eigenvalues | Constants | Complement | Invariants

Journal Article

Journal of Mathematical Inequalities, ISSN 1846-579X, 06/2018, Volume 12, Issue 2, pp. 315 - 323

In this paper we present some reverses of the Golden-Thompson type inequalities: Let H and K be Hermitian matrices such that e(s)e(H )<= ols e(K) <= ols e(t)e(H...

Generalized Kantorovich constant | Golden-Thompson inequality | Specht ratio | Unitarily invariant norm | Geometric mean | Ando-Hiai inequality | Olson order | Eigenvalue inequality | unitarily invariant norm | MATHEMATICS | MATHEMATICS, APPLIED | generalized Kantorovich constant | eigenvalue inequality | OPERATORS | geometric mean

Generalized Kantorovich constant | Golden-Thompson inequality | Specht ratio | Unitarily invariant norm | Geometric mean | Ando-Hiai inequality | Olson order | Eigenvalue inequality | unitarily invariant norm | MATHEMATICS | MATHEMATICS, APPLIED | generalized Kantorovich constant | eigenvalue inequality | OPERATORS | geometric mean

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 02/2013, Volume 438, Issue 4, pp. 1580 - 1586

The grand Furuta inequality has the following satellite (SGF;t∈[0,1]), given as a mean theoretic expression:A⩾B>0,t∈[0,1]⇒A-r+t#1-t+r(p-t)s+r(At♮sBp)⩽Bforr⩾t;p,s⩾1,where #α is the α...

Ando-Hiai inequality | 47A64 | Primary 47A63 | Furuta inequality and grand Furuta inequality | Positive operators | Operator mean | MATHEMATICS | MATHEMATICS, APPLIED | MEAN THEORETIC APPROACH | EXTENSION | Equality

Ando-Hiai inequality | 47A64 | Primary 47A63 | Furuta inequality and grand Furuta inequality | Positive operators | Operator mean | MATHEMATICS | MATHEMATICS, APPLIED | MEAN THEORETIC APPROACH | EXTENSION | Equality

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 09/1996, Volume 124, Issue 9, pp. 2751 - 2756

Very recently, Furuta obtained the grand Furuta inequality which is a parameteric formula interpolating the Furuta inequality and the Ando-Hiai inequality as follows : If A \ge B...

Mathematical theorems | Linear inequalities | Mathematical inequalities | Mathematical functions | Increasing functions | Operator theory | Decreasing functions | Ando-Hiai inequality | Furuta inequality | Löwner-Heinz inequality | Positive operators | Grand Furuta inequality | MATHEMATICS | MATHEMATICS, APPLIED | grand Furuta inequality | Lowner-Heinz inequality | OPERATOR-FUNCTIONS | ANDO THEOREM

Mathematical theorems | Linear inequalities | Mathematical inequalities | Mathematical functions | Increasing functions | Operator theory | Decreasing functions | Ando-Hiai inequality | Furuta inequality | Löwner-Heinz inequality | Positive operators | Grand Furuta inequality | MATHEMATICS | MATHEMATICS, APPLIED | grand Furuta inequality | Lowner-Heinz inequality | OPERATOR-FUNCTIONS | ANDO THEOREM

Journal Article

Journal of Mathematical Inequalities, ISSN 1846-579X, 09/2012, Volume 6, Issue 3, pp. 481 - 491

Very recently, Yamazaki has obtained an excellent generalization of Ando-Hiai inequality and a characterization of chaotic order...

Riemannian mean | Furuta inequality and Ando-Hiai inequality | Positive definite matrix | MATHEMATICS | MATHEMATICS, APPLIED

Riemannian mean | Furuta inequality and Ando-Hiai inequality | Positive definite matrix | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Banach journal of mathematical analysis, ISSN 1735-8787, 2010, Volume 4, Issue 1, pp. 87 - 91

In this paper, we show a complement of Ando-Hiai inequality: Let A and B be positive invertible operators on a Hilbert space H and alpha is an element of [0, 1...

Ando-Hiai inequality | Ando-Hiai inequaqlity | Geometric mean | Positive operator | MATHEMATICS | MATHEMATICS, APPLIED | positive operator | geometric mean | Inequalities (Mathematics) | Hilbert space | Research | Operator theory

Ando-Hiai inequality | Ando-Hiai inequaqlity | Geometric mean | Positive operator | MATHEMATICS | MATHEMATICS, APPLIED | positive operator | geometric mean | Inequalities (Mathematics) | Hilbert space | Research | Operator theory

Journal Article

数理解析研究所講究録, ISSN 1880-2818, 05/2014, Volume 1893, pp. 126 - 135

Journal Article

ANNALS OF FUNCTIONAL ANALYSIS, ISSN 2008-8752, 2010, Volume 1, Issue 2, pp. 28 - 45

This article is devoted to a brief survey of Furuta inequality and its related topics...

MATHEMATICS | MATHEMATICS, APPLIED | Lowner-Heinz inequality | Furuta inequality | TANAHASHIS RESULT | Grand Furuta inequality | Ando-Hiai inequality | CHAOTIC ORDER | chaotic order and operator geometric mean | SIMPLIFIED PROOF

MATHEMATICS | MATHEMATICS, APPLIED | Lowner-Heinz inequality | Furuta inequality | TANAHASHIS RESULT | Grand Furuta inequality | Ando-Hiai inequality | CHAOTIC ORDER | chaotic order and operator geometric mean | SIMPLIFIED PROOF

Journal Article

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