Mathematical Inequalities and Applications, ISSN 1331-4343, 2004, Volume 7, Issue 1, pp. 113 - 125

... to A(lambda) for lambda is an element of [0, 1]. In this note, we prove that the estimation of the converse Young operator inequality is obtained by using Specht's ratio...

Logarithmic mean | Specht's ratio | Arithmetic mean | Geometric mean | Hölder-McCarthy inequality | Young's inequality | MATHEMATICS | arithmetic mean | logarithmic mean | Holder-McCarthy inequality | OPERATORS | geometric mean

Logarithmic mean | Specht's ratio | Arithmetic mean | Geometric mean | Hölder-McCarthy inequality | Young's inequality | MATHEMATICS | arithmetic mean | logarithmic mean | Holder-McCarthy inequality | OPERATORS | geometric mean

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 02/2013, Volume 438, Issue 4, pp. 1711 - 1726

.... Among others, the Specht ratio plays an important role in our discussion, which is the upper bound of a ratio type reverse of the weighted arithmetic...

Positive linear map | Specht ratio | Chaotic geometric mean | Ando–Li–Mathias geometric mean | Reverse inequality | Mond–Shisha difference | Positive operator | Mond-Shisha difference | Ando-Li-Mathias geometric mean | MATHEMATICS | MATHEMATICS, APPLIED | MAPS

Positive linear map | Specht ratio | Chaotic geometric mean | Ando–Li–Mathias geometric mean | Reverse inequality | Mond–Shisha difference | Positive operator | Mond-Shisha difference | Ando-Li-Mathias geometric mean | MATHEMATICS | MATHEMATICS, APPLIED | MAPS

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: The Ando-Li-Mathias geometric mean, the...

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

Linear Algebra and Its Applications, ISSN 0024-3795, 2006, Volume 416, Issue 2, pp. 688 - 695

In this paper, we shall extend Kantorovich inequality. This is an estimate by using the geometric mean of n-operators which have been defined by...

Geometric mean of n-operators | Kantorovich inequality | Arithmetic–geometric means inequality | Specht’s ratio | Specht's ratio | Arithmetic-geometric means inequality | arithmetic-geometric means inequality | MATHEMATICS, APPLIED | geometric mean of n-operators | Equality

Geometric mean of n-operators | Kantorovich inequality | Arithmetic–geometric means inequality | Specht’s ratio | Specht's ratio | Arithmetic-geometric means inequality | arithmetic-geometric means inequality | MATHEMATICS, APPLIED | geometric mean of n-operators | Equality

Journal Article

Journal of the Egyptian Mathematical Society, ISSN 1110-256X, 2012, Volume 20, Issue 1, pp. 46 - 49

...-weighted geometric mean and Specht’s ratio. As a corollary, we also show that the ν-weighted geometric mean is greater than the product of the ν...

Operator mean and operator inequality | Specht’s ratio | Young inequality | Positive operator

Operator mean and operator inequality | Specht’s ratio | Young inequality | Positive operator

Journal Article

Journal of Mathematical Inequalities, ISSN 1846-579X, 2011, Volume 5, Issue 4, pp. 551 - 556

The Specht ratio S(h) is the optimal constant in the reverse of the arithmetic-geometric mean inequality, i.e., if 0 < m <= a, b <= M and h = M/m, then (1 - mu)a + mu b <= S(h)a(1-mu) b(mu...

Operator inequality | Specht ratio | Operator means | Kantorovich constant | Young inequality | Arithmetic-geometric-harmonic mean inequality | MATHEMATICS | MATHEMATICS, APPLIED | operator inequality | operator means | arithmetic-geometric-harmonic mean inequality

Operator inequality | Specht ratio | Operator means | Kantorovich constant | Young inequality | Arithmetic-geometric-harmonic mean inequality | MATHEMATICS | MATHEMATICS, APPLIED | operator inequality | operator means | arithmetic-geometric-harmonic mean inequality

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2006, Volume 412, Issue 2, pp. 526 - 537

Recently Tsallis relative operator entropy T p ( A∣ B) and Tsallis relative entropy D p ( A∥ B) are discussed by Furuichi–Yanagi–Kuriyama. We shall show two...

Generalized Kantorovich constant | Tsallis relative operator entropy | Specht ratio | Relative operator entropy | Tsallis relative entropy | Umegaki relative entropy | MATHEMATICS, APPLIED | relative operator entropy | generalized Kantorovich constant

Generalized Kantorovich constant | Tsallis relative operator entropy | Specht ratio | Relative operator entropy | Tsallis relative entropy | Umegaki relative entropy | MATHEMATICS, APPLIED | relative operator entropy | generalized Kantorovich constant

Journal Article

Mathematical Inequalities and Applications, ISSN 1331-4343, 2003, Volume 6, Issue 3, pp. 521 - 530

.... We show a very interesting new relation between Specht ratio S(1) and Kantorovich constant K(p) : S(1) = e(K)' ((1...

Specht ratio | Kantorovich constant | MATHEMATICS | OPERATOR INEQUALITIES

Specht ratio | Kantorovich constant | MATHEMATICS | OPERATOR INEQUALITIES

Journal Article

9.
Full Text
Reverse inequalities involving two relative operator entropies and two relative entropies

Linear Algebra and Its Applications, ISSN 0024-3795, 2005, Volume 403, Issue 1-3, pp. 24 - 30

..., in particular log S ( 1 ) Tr [ A ] + S ( A , B ) ⩾ - Tr [ S ^ ( A | B ) ] ⩾ S ( A , B ) where S(1) is the Specht ratio defined...

Generalized Kantorovich constant | Tsallis relative operator entropy | Specht ratio | Relative operator entropy | Tsallis relative entropy | Umegaki relative entropy | MATHEMATICS, APPLIED | generalized Kantorovich constants | relative operator entropy

Generalized Kantorovich constant | Tsallis relative operator entropy | Specht ratio | Relative operator entropy | Tsallis relative entropy | Umegaki relative entropy | MATHEMATICS, APPLIED | generalized Kantorovich constants | relative operator entropy

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2004, Volume 377, Issue 1-3, pp. 69 - 81

As a converse of the arithmetic and geometric mean inequality, Specht gave the ratio of the arithmetic one by the geometric one in 1960...

Specht ratio | Chaotic order | Furuta inequality | Kantorovich inequality | Löwner–Heinz theorem | Grand Furuta inequality | Löwner-Heinz theorem | chaotic order | MATHEMATICS, APPLIED | grand Furuta inequality | MEAN THEORETIC APPROACH | Lowner-Heinz theorem | SIMPLIFIED PROOF

Specht ratio | Chaotic order | Furuta inequality | Kantorovich inequality | Löwner–Heinz theorem | Grand Furuta inequality | Löwner-Heinz theorem | chaotic order | MATHEMATICS, APPLIED | grand Furuta inequality | MEAN THEORETIC APPROACH | Lowner-Heinz theorem | SIMPLIFIED PROOF

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 12/2003, Volume 375, pp. 251 - 273

An operator means a bounded linear operator on a Hilbert space H. We obtained the basic property between Specht ratio S(1...

MATHEMATICS | Specht ratio | MATHEMATICS, APPLIED | MAPS | FURUTA | Kantorovich inequality

MATHEMATICS | Specht ratio | MATHEMATICS, APPLIED | MAPS | FURUTA | Kantorovich inequality

Journal Article

Journal of Mathematical Inequalities, ISSN 1846-579X, 2011, Volume 5, Issue 1, pp. 21 - 31

In this paper, we show refined Young inequalities for two positive operators. Our results refine the ordering relations among the arithmetic mean, the...

Reverse inequality | Young inequality | Specht's ratio and operator inequality | Operator mean | Positive operator | MATHEMATICS | MATHEMATICS, APPLIED | positive operator | reverse inequality | operator mean

Reverse inequality | Young inequality | Specht's ratio and operator inequality | Operator mean | Positive operator | MATHEMATICS | MATHEMATICS, APPLIED | positive operator | reverse inequality | operator mean

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2003, Volume 375, pp. 251 - 273

An operator means a bounded linear operator on a Hilbert space H. We obtained the basic property between Specht ratio S(1...

Specht ratio | Kantorovich inequality

Specht ratio | Kantorovich inequality

Journal Article

Journal of Mathematical Inequalities, ISSN 1846-579X, 2017, Volume 11, Issue 2, pp. 301 - 322

In this paper we develop a general method for improving Jensen-type inequalities for convex and, even more generally, for piecewise convex functions. Our main...

Specht ratio | Kantorovich constant | Geometric mean | Young inequality | Heinz mean | Convex function | Arithmetic mean | Jensen inequality | MATHEMATICS, APPLIED | geometric mean | MATHEMATICS | OPERATOR INEQUALITIES | arithmetic mean | IMPROVED YOUNG | HEINZ INEQUALITIES

Specht ratio | Kantorovich constant | Geometric mean | Young inequality | Heinz mean | Convex function | Arithmetic mean | Jensen inequality | MATHEMATICS, APPLIED | geometric mean | MATHEMATICS | OPERATOR INEQUALITIES | arithmetic mean | IMPROVED YOUNG | HEINZ INEQUALITIES

Journal Article

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

..., S(t) is the so called Specht's ratio and <=(ols) is the so called Olson order. The same inequalities are also provided with other constants...

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

Mathematical Inequalities and Applications, ISSN 1331-4343, 04/2016, Volume 19, Issue 2, pp. 757 - 764

<= qA, then for all a is an element of [0,1] f(A) (alpha)f (B) <= max {S(p), S(q)}f(A(alpha)B), where S(t) is the so called Specht's ratio...

Norm inequality | Majorization | Operator monotone function | α-arithmetic (α-geometric | Operator monotone decreasing function | Specht's ratio | α-harmonic) operator mean | Operator convex function | operator monotone decreasing function | norm inequality | MATHEMATICS | CONCAVITY | operator convex function | alpha-arithmetic (alpha-geometric, alpha-harmonic) operator mean | NORMS | majorization

Norm inequality | Majorization | Operator monotone function | α-arithmetic (α-geometric | Operator monotone decreasing function | Specht's ratio | α-harmonic) operator mean | Operator convex function | operator monotone decreasing function | norm inequality | MATHEMATICS | CONCAVITY | operator convex function | alpha-arithmetic (alpha-geometric, alpha-harmonic) operator mean | NORMS | majorization

Journal Article

International Journal of Mathematical Analysis, ISSN 1312-8876, 2015, Volume 9, Issue 41-44, pp. 2111 - 2119

Journal Article

Mathematical Inequalities and Applications, ISSN 1331-4343, 2000, Volume 3, Issue 2, pp. 259 - 268

As a characterization of chaotic order, we showed "If Ml greater than or equal to B greater than or equal to ml > 0, then log A greater than or equal to log B...

Chaotic order | Specht's ratio | Positive operator | chaotic order | MATHEMATICS | OPERATOR INEQUALITIES | positive operator

Chaotic order | Specht's ratio | Positive operator | chaotic order | MATHEMATICS | OPERATOR INEQUALITIES | positive operator

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 12/2003, Volume 375, Issue 1-3, pp. 251 - 273

An operator means a bounded linear operator on a Hilbert space H. We obtained the basic property between Specht ratio S(1...

Specht ratio | Kantorovich inequality

Specht ratio | Kantorovich inequality

Journal Article

Mathematical inequalities & applications, ISSN 1331-4343, 2002, Volume 5, Issue 3, pp. 573 - 582

We prove a Golden-Thompson type inequality via Specht's ratio: Let H and K be selfadjoint operators on a Hilbert space H satisfying M1 greater than or equal...

Operator inequality | Golden-Thompson inequality | Specht's ratio | Kantorovich type inequality | Positive operator | MATHEMATICS | positive operator | operator inequality

Operator inequality | Golden-Thompson inequality | Specht's ratio | Kantorovich type inequality | Positive operator | MATHEMATICS | positive operator | operator inequality

Journal Article

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