Mathematische annalen, ISSN 1432-1807, 2011, Volume 353, Issue 4, pp. 1453 - 1467

An attractive candidate for the geometric mean of m positive definite matrices A
1, . . . , A
m
is their Riemannian barycentre G. One of its important operator...

53C20 | Mathematics, general | 15B48 | Mathematics | 47A64 | MATHEMATICS

53C20 | Mathematics, general | 15B48 | Mathematics | 47A64 | MATHEMATICS

Journal Article

Mathematische Annalen, ISSN 0025-5831, 7/2011, Volume 350, Issue 3, pp. 611 - 630

We study operator log-convex functions on (0, ∞), and prove that a continuous nonnegative function on (0, ∞) is operator log-convex if and only if it is...

Mathematics, general | Mathematics | 47A64 | 15A45 | 47A63 | MATHEMATICS | Mathematics - Functional Analysis

Mathematics, general | Mathematics | 47A64 | 15A45 | 47A63 | MATHEMATICS | Mathematics - Functional Analysis

Journal Article

Mathematische Zeitschrift, ISSN 1432-1823, 2017, Volume 289, Issue 1-2, pp. 445 - 454

The aim of this paper is to find some sufficient conditions for positivity of block matrices of positive operators. It is shown that for positive operators...

15A45 | Mathematics, general | Operator monotone function | Mathematics | 47A64 | Positive block matrix | 47A63 | Operator mean | MATHEMATICS | INEQUALITIES

15A45 | Mathematics, general | Operator monotone function | Mathematics | 47A64 | Positive block matrix | 47A63 | Operator mean | MATHEMATICS | INEQUALITIES

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 1/2019, Volume 42, Issue 1, pp. 267 - 284

In this paper, we study the further improvements of the reverse Young and Heinz inequalities for the wider range of v, namely
$$v\in \mathbb {R}$$
v
∈
R
....

Young’s inequality | Operator inequality | 15A39 | Mathematics, general | Mathematics | 47A64 | Applications of Mathematics | 47A63 | Heinz inequality | 47A60 | MATHEMATICS | OPERATOR | Young's inequality | Mathematics - Classical Analysis and ODEs

Young’s inequality | Operator inequality | 15A39 | Mathematics, general | Mathematics | 47A64 | Applications of Mathematics | 47A63 | Heinz inequality | 47A60 | MATHEMATICS | OPERATOR | Young's inequality | Mathematics - Classical Analysis and ODEs

Journal Article

5.
Full Text
Transformations Preserving Norms of Means of Positive Operators and Nonnegative Functions

Integral equations and operator theory, ISSN 0378-620X, 10/2015, Volume 83, Issue 2, pp. 271 - 290

Motivated by recent investigations on norm-additive and spectrally multiplicative maps on various spaces of functions, in this paper we determine all bijective...

Secondary: 47A64 | 26E60 | Primary: 47B49 | means of functions | MATHEMATICS | symmetric norms | ALGEBRAS | MAPS | operator means | Preservers | AUTOMORPHISMS | Analysis | Algebra

Secondary: 47A64 | 26E60 | Primary: 47B49 | means of functions | MATHEMATICS | symmetric norms | ALGEBRAS | MAPS | operator means | Preservers | AUTOMORPHISMS | Analysis | Algebra

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 8/2019, Volume 93, Issue 4, pp. 669 - 690

The main objective of the present paper is a study of mutual bounds for the Jensen operator inequality and the Lah–Ribarič operator inequality for the classes...

Lipschitzian function | Primary 47A63 | Analysis | Mathematics | 47A64 | Lah–Ribarič operator inequality | Convexity | Combinatorics | Operator convexity | Jensen operator inequality | Bounded function | MATHEMATICS | MATHEMATICS, APPLIED | Lah-Ribari operator inequality | Mathematical functions | Mathematical analysis | Arithmetic

Lipschitzian function | Primary 47A63 | Analysis | Mathematics | 47A64 | Lah–Ribarič operator inequality | Convexity | Combinatorics | Operator convexity | Jensen operator inequality | Bounded function | MATHEMATICS | MATHEMATICS, APPLIED | Lah-Ribari operator inequality | Mathematical functions | Mathematical analysis | Arithmetic

Journal Article

7.
Full Text
Extensions of interpolation between the arithmetic-geometric mean inequality for matrices

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 10

In this paper, we present some extensions of interpolation between the arithmetic-geometric means inequality. Among other inequalities, it is shown that if A,...

unitarily invariant norm | Cauchy-Schwarz inequality | Analysis | arithmetic-geometric mean | Mathematics, general | Mathematics | 47A64 | Applications of Mathematics | 15A60 | Hilbert-Schmidt norm | MATHEMATICS | MATHEMATICS, APPLIED | YOUNG INEQUALITIES | OPERATORS | Interpolation | Real numbers | Continuity (mathematics) | Inequalities | Inequality | Arithmetic | Research

unitarily invariant norm | Cauchy-Schwarz inequality | Analysis | arithmetic-geometric mean | Mathematics, general | Mathematics | 47A64 | Applications of Mathematics | 15A60 | Hilbert-Schmidt norm | MATHEMATICS | MATHEMATICS, APPLIED | YOUNG INEQUALITIES | OPERATORS | Interpolation | Real numbers | Continuity (mathematics) | Inequalities | Inequality | Arithmetic | Research

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 08/2018, Volume 68, Issue 4, pp. 803 - 810

The main objective of the present paper, is to obtain some new versions of Young-type inequalities with respect to two weighted arithmetic and geometric means...

Kantorovich constant | Secondary 47A64 | Primary 47A63 | Young inequality | 47B65 | Heinz mean | weighted arithmetic and geometric mean | strictly positive operator | MATHEMATICS | MATRICES | Arrays | Inequalities

Kantorovich constant | Secondary 47A64 | Primary 47A63 | Young inequality | 47B65 | Heinz mean | weighted arithmetic and geometric mean | strictly positive operator | MATHEMATICS | MATRICES | Arrays | Inequalities

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 9

This note aims to generalize the reverse weighted arithmetic–geometric mean inequality of n positive invertible operators due to Lawson and Lim. In addition,...

Lawson–Lim geometric mean | Kantorovich constant | 15A45 | Analysis | Ando–Li–Mathias geometric mean | Mathematics, general | Mathematics | 47A64 | Applications of Mathematics | Karcher mean | 47A63 | MATHEMATICS | MATHEMATICS, APPLIED | Ando-Li-Mathias geometric mean | KANTOROVICH INEQUALITY | Lawson-Lim geometric mean | Operators | Research

Lawson–Lim geometric mean | Kantorovich constant | 15A45 | Analysis | Ando–Li–Mathias geometric mean | Mathematics, general | Mathematics | 47A64 | Applications of Mathematics | Karcher mean | 47A63 | MATHEMATICS | MATHEMATICS, APPLIED | Ando-Li-Mathias geometric mean | KANTOROVICH INEQUALITY | Lawson-Lim geometric mean | Operators | Research

Journal Article

Positivity, ISSN 1385-1292, 7/2018, Volume 22, Issue 3, pp. 773 - 781

The famous Hardy inequality asserts that if f is a non-negative p-integrable $$(p>1)$$
(p>1)
function on $$(0,\infty )$$
(0,∞)
, then $$\begin{aligned} \int...

Operator log-convex | Operator Theory | Fourier Analysis | Secondary 47A64 | Potential Theory | Operator Hardy inequality | Weakly measurable map | Calculus of Variations and Optimal Control; Optimization | Primary 47A63 | Mathematics | Econometrics | MATHEMATICS | NONCOMMUTATIVE HARDY | Equality | Operators (mathematics) | Hilbert space | Inequality

Operator log-convex | Operator Theory | Fourier Analysis | Secondary 47A64 | Potential Theory | Operator Hardy inequality | Weakly measurable map | Calculus of Variations and Optimal Control; Optimization | Primary 47A63 | Mathematics | Econometrics | MATHEMATICS | NONCOMMUTATIVE HARDY | Equality | Operators (mathematics) | Hilbert space | Inequality

Journal Article

Mediterranean journal of mathematics, ISSN 1660-5454, 2017, Volume 14, Issue 5, pp. 1 - 18

In this article, we present several inequalities treating operator means and the Cauchy–Schwarz inequality. In particular, we present some new comparisons...

unitarily invariant norm | normalized Jensen functional | Norm inequality | Mathematics, general | Mathematics | 47A64 | 15A60 | 47A30 | 47A63 | operator mean | Heinz inequality | MATHEMATICS | MATHEMATICS, APPLIED | REFINEMENTS | OPERATOR

unitarily invariant norm | normalized Jensen functional | Norm inequality | Mathematics, general | Mathematics | 47A64 | 15A60 | 47A30 | 47A63 | operator mean | Heinz inequality | MATHEMATICS | MATHEMATICS, APPLIED | REFINEMENTS | OPERATOR

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 20

In this paper, we study some complementary inequalities to Jensen’s inequality for self-adjoint operators, unital positive linear mappings, and real valued...

positive linear mapping | convex function | Mathematics | 47A64 | Mond-Pečarić method | 47A63 | self-adjoint operator | 47B15 | converse of Jensen’s operator inequality | Analysis | Mathematics, general | 46L05 | Applications of Mathematics | converse of Jensen's operator inequality | QUASI-ARITHMETIC MEANS | MATHEMATICS | Mond-Pecaric method | MATHEMATICS, APPLIED | POSITIVE LINEAR-MAPS | CONVERSES | Research

positive linear mapping | convex function | Mathematics | 47A64 | Mond-Pečarić method | 47A63 | self-adjoint operator | 47B15 | converse of Jensen’s operator inequality | Analysis | Mathematics, general | 46L05 | Applications of Mathematics | converse of Jensen's operator inequality | QUASI-ARITHMETIC MEANS | MATHEMATICS | Mond-Pecaric method | MATHEMATICS, APPLIED | POSITIVE LINEAR-MAPS | CONVERSES | Research

Journal Article

Annals of functional analysis, ISSN 2008-8752, 2017, Volume 8, Issue 1, pp. 142 - 151

Suppose that X, Y are positive random variables and m is a numerical (commutative) mean. We prove that the inequality E(m(X, Y)) <= m(E(X), E(Y)) holds if and...

Operator means | Random matrices | Numerical means | Concavity | MATHEMATICS | MATHEMATICS, APPLIED | random matrices | numerical means | operator means | MATRICES | PERSPECTIVES | concavity | Mathematics - Probability

Operator means | Random matrices | Numerical means | Concavity | MATHEMATICS | MATHEMATICS, APPLIED | random matrices | numerical means | operator means | MATRICES | PERSPECTIVES | concavity | Mathematics - Probability

Journal Article

Positivity, ISSN 1385-1292, 3/2017, Volume 21, Issue 1, pp. 299 - 327

We study a mapping
$$\tau _G$$
τ
G
of the cone
$${\mathbf B}^+({\mathcal H})$$
B
+
(
H
)
of bounded nonnegative self-adjoint operators in a complex Hilbert...

Mathematics | 47A64 | Iterates | Operator Theory | Fourier Analysis | Lebesgue type decomposition | Potential Theory | Calculus of Variations and Optimal Control; Optimization | 47A05 | 46B25 | Parallel sum | Econometrics | Fixed point | MATHEMATICS | Analysis | Numerical analysis | Studies | Hilbert space | Mathematical analysis

Mathematics | 47A64 | Iterates | Operator Theory | Fourier Analysis | Lebesgue type decomposition | Potential Theory | Calculus of Variations and Optimal Control; Optimization | 47A05 | 46B25 | Parallel sum | Econometrics | Fixed point | MATHEMATICS | Analysis | Numerical analysis | Studies | Hilbert space | Mathematical analysis

Journal Article

Journal of elasticity, ISSN 1573-2681, 2006, Volume 82, Issue 3, pp. 273 - 296

In this paper we present properly invariant averaging procedures for symmetric positive-definite tensors which are based on different measures of nearness of...

26E60 | Kullback–Leibler mean | 74B05 | averaging | 15A48 | 47A64 | elasticity tensor | geometric mean | symmetric positive-definite tensors | Elasticity tensor | Averaging | Kullback-Leibler mean | Geometric mean | Symmetric positive-definite tensors | SINGLE-CRYSTAL | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | MATERIALS SCIENCE, MULTIDISCIPLINARY | Studies

26E60 | Kullback–Leibler mean | 74B05 | averaging | 15A48 | 47A64 | elasticity tensor | geometric mean | symmetric positive-definite tensors | Elasticity tensor | Averaging | Kullback-Leibler mean | Geometric mean | Symmetric positive-definite tensors | SINGLE-CRYSTAL | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | MATERIALS SCIENCE, MULTIDISCIPLINARY | Studies

Journal Article

Georgian Mathematical Journal, ISSN 1072-947X, 03/2018, Volume 25, Issue 1, pp. 93 - 107

The aim of this paper is to present a comprehensive study of operator
-convex functions.
Let
, and
for some
or
.
A continuous function
is called operator...

26A51 | Jensen operator functional | Jensen–Mercer inequality | 46L05 | 47A64 | Jensen inequality | Choi–Davis–Jensen inequality | 47A63 | MATHEMATICS | JENSENS INEQUALITY | REFINEMENTS | Jensen-Mercer inequality | MERCERS TYPE | operator m-convex | Choi-Davis-Jensen inequality

26A51 | Jensen operator functional | Jensen–Mercer inequality | 46L05 | 47A64 | Jensen inequality | Choi–Davis–Jensen inequality | 47A63 | MATHEMATICS | JENSENS INEQUALITY | REFINEMENTS | Jensen-Mercer inequality | MERCERS TYPE | operator m-convex | Choi-Davis-Jensen inequality

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 5/2016, Volume 85, Issue 1, pp. 63 - 90

We show that several known facts concerning roots of matrices generalize to operator algebras and Banach algebras. We show for example that the so-called...

numerical range | nonselfadjoint operator algebra | accretive operator | Secondary 15A24 | Newton method for roots | Primary 47A64 | Roots | fractional powers | 47B44 | 47A12 | Mathematics | sectorial operator | 47A63 | sign of operator | 47A60 | geometric mean | 47L30 | functional calculus | Analysis | 65F30 | 49M15 | 15A60 | 47L10 | binomial method for square root | POWERS | MATHEMATICS | NUMERICAL RANGES | MATRICES | Algebra

numerical range | nonselfadjoint operator algebra | accretive operator | Secondary 15A24 | Newton method for roots | Primary 47A64 | Roots | fractional powers | 47B44 | 47A12 | Mathematics | sectorial operator | 47A63 | sign of operator | 47A60 | geometric mean | 47L30 | functional calculus | Analysis | 65F30 | 49M15 | 15A60 | 47L10 | binomial method for square root | POWERS | MATHEMATICS | NUMERICAL RANGES | MATRICES | Algebra

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

Integral Equations and Operator Theory, ISSN 0378-620X, 1/2015, Volume 81, Issue 1, pp. 53 - 95

For a bounded non-negative self-adjoint operator acting in a complex, infinite-dimensional, separable Hilbert space
$${\mathcal{H}}$$
H
and possessing a dense...

parallel addition | Operator range | shorted operator | Mathematics | 47A20 | 47A64 | von Neumann Theorem | Kreĭn extension | 47A07 | 47B25 | Van Daele–Schmüdgen theorem | 47A05 | Analysis | lifting | Friedrichs extension | Van Daele–Schm¨udgen theorem | Kre˘in extension | QUASI-SECTORIAL CONTRACTIONS | Krein extension | RESTRICTIONS | MATHEMATICS | PRODUCT FORMULA | SYMMETRIC-OPERATORS | Van Daele-Schmudgen theorem | MATRICES | DOMAINS | RANGE | Functional Analysis

parallel addition | Operator range | shorted operator | Mathematics | 47A20 | 47A64 | von Neumann Theorem | Kreĭn extension | 47A07 | 47B25 | Van Daele–Schmüdgen theorem | 47A05 | Analysis | lifting | Friedrichs extension | Van Daele–Schm¨udgen theorem | Kre˘in extension | QUASI-SECTORIAL CONTRACTIONS | Krein extension | RESTRICTIONS | MATHEMATICS | PRODUCT FORMULA | SYMMETRIC-OPERATORS | Van Daele-Schmudgen theorem | MATRICES | DOMAINS | RANGE | Functional Analysis

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 4/2014, Volume 8, Issue 4, pp. 875 - 923

The block operator CMV matrices and their sub-matrices are applied to the description of all solutions to the Schur interpolation problem for contractive...

Schur problem | 30E05 | 47A56 | Mathematics | 47A64 | Toeplitz matrix | Contraction | Conservative system | Operator Theory | 47N70 | 47A48 | Analysis | 47A57 | 47B35 | Mathematics, general | Kreĭn shorted operator | Schur class function | Transfer function | CMV matrix | Schur parameters | Kreǐn shorted operator | MATHEMATICS | MATHEMATICS, APPLIED | Krein shorted operator | PARAMETRIZATION

Schur problem | 30E05 | 47A56 | Mathematics | 47A64 | Toeplitz matrix | Contraction | Conservative system | Operator Theory | 47N70 | 47A48 | Analysis | 47A57 | 47B35 | Mathematics, general | Kreĭn shorted operator | Schur class function | Transfer function | CMV matrix | Schur parameters | Kreǐn shorted operator | MATHEMATICS | MATHEMATICS, APPLIED | Krein shorted operator | PARAMETRIZATION

Journal Article

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