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ando-hiai inequality (19) 19
mathematics (19) 19
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operator mean (10) 10
ando–hiai inequality (9) 9
geometric mean (7) 7
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15a60 (1) 1
47a60 (1) 1
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a ms subject classification: 47a63 and 47b15 (1) 1
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ando-hiai inequality and grand furuta inequality (1) 1
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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
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
Journal Article
Linear algebra and its applications, ISSN 0024-3795, 2008, Volume 429, Issue 7, pp. 1546 - 1554
Journal Article
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
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 03/2015, Volume 63, Issue 3, pp. 636 - 649
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
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
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
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
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
Journal Article
Operators and Matrices, ISSN 1846-3886, 09/2012, Volume 6, Issue 3, pp. 577 - 588
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 03/2016, Volume 64, Issue 3, pp. 512 - 526
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
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
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
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
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
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
Journal Article
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