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

The American Mathematical Monthly, ISSN 0002-9890, 10/2019, Volume 126, Issue 9, pp. 809 - 815

We describe a rather striking extension of a wide class of inequalities. Some famous classical inequalities, such as those of Hardy and Hilbert, equate to the...

Secondary 15A45 | MSC: Primary 47A63 | MATHEMATICS | MSC

Secondary 15A45 | MSC: Primary 47A63 | MATHEMATICS | MSC

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 11

In this paper, we generalize some Schatten p-norm inequalities for accretive-dissipative matrices obtained by Kittaneh and Sakkijha. Moreover, we present some...

Accretive-dissipative matrix | 15A45 | Schatten p -norm | Analysis | Mathematics, general | Mathematics | 15A15 | Applications of Mathematics | Sector matrix | Inequality | Schatten p-norm | MATHEMATICS | MATHEMATICS, APPLIED | SINGULAR-VALUE INEQUALITIES | Inequalities | Research

Accretive-dissipative matrix | 15A45 | Schatten p -norm | Analysis | Mathematics, general | Mathematics | 15A15 | Applications of Mathematics | Sector matrix | Inequality | Schatten p-norm | MATHEMATICS | MATHEMATICS, APPLIED | SINGULAR-VALUE INEQUALITIES | Inequalities | Research

Journal Article

Duke mathematical journal, ISSN 0012-7094, 02/2013, Volume 162, Issue 3, pp. 579 - 625

Starting from the quantitative stability result of Bianchi and Egnell for the 2-Sobolev inequality, we deduce several different stability results for a...

MATHEMATICS | SHARP SOBOLEV | MODEL | SOBOLEV INEQUALITY | Mathematics - Analysis of PDEs | 49M20 | 15A45

MATHEMATICS | SHARP SOBOLEV | MODEL | SOBOLEV INEQUALITY | Mathematics - Analysis of PDEs | 49M20 | 15A45

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 12/2015, Volume 487, pp. 260 - 267

In this paper, we will show a new characterization of operator monotone functions by a matrix reverse Cauchy inequality.

Reverse Cauchy inequality | Characterization of operator monotonicity | Mean of positive matrices | 15A45 | MSC 46L30 | MATHEMATICS | MATHEMATICS, APPLIED

Reverse Cauchy inequality | Characterization of operator monotonicity | Mean of positive matrices | 15A45 | MSC 46L30 | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Archiv der Mathematik, ISSN 1420-8938, 2014, Volume 104, Issue 1, pp. 93 - 100

Haynsworth (Proc Am Math Soc 24:512–516, 1970) used a result of the Schur complement to refine a determinant inequality for positive definite matrices....

Numerical range | 15A45 | Determinant inequality | Sector | Mathematics, general | Mathematics | 15A60 | Schur complement | DETERMINANTAL INEQUALITIES | MATHEMATICS | GAUSSIAN-ELIMINATION | ACCRETIVE-DISSIPATIVE MATRICES | GROWTH-FACTOR

Numerical range | 15A45 | Determinant inequality | Sector | Mathematics, general | Mathematics | 15A60 | Schur complement | DETERMINANTAL INEQUALITIES | MATHEMATICS | GAUSSIAN-ELIMINATION | ACCRETIVE-DISSIPATIVE MATRICES | GROWTH-FACTOR

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 4/2018, Volume 12, Issue 4, pp. 1057 - 1142

The (classical) truncated moment problem, extensively studied by Curto and Fialkow, asks to characterize when a finite sequence of real numbers indexes by...

15-04 | Mathematics | Flat extensions | Secondary 11E25 | 44A60 | Moment matrix | 13J30 | Non-commutative polynomial | Operator Theory | Affine linear transformations | 15A45 | Analysis | Mathematics, general | Primary 47A57 | Truncated moment problem | MATHEMATICS, APPLIED | HERMITIAN SQUARES | SUMS | POSITIVE POLYNOMIALS | MATHEMATICS | POSITIVSTELLENSATZ | MATRICES | OPTIMIZATION | Mathematics - Functional Analysis

15-04 | Mathematics | Flat extensions | Secondary 11E25 | 44A60 | Moment matrix | 13J30 | Non-commutative polynomial | Operator Theory | Affine linear transformations | 15A45 | Analysis | Mathematics, general | Primary 47A57 | Truncated moment problem | MATHEMATICS, APPLIED | HERMITIAN SQUARES | SUMS | POSITIVE POLYNOMIALS | MATHEMATICS | POSITIVSTELLENSATZ | MATRICES | OPTIMIZATION | Mathematics - Functional Analysis

Journal Article

Advances in applied mathematics, ISSN 0196-8858, 09/2016, Volume 80, pp. 1 - 23

In the convergence analysis of numerical methods for solving partial differential equations (such as finite element methods) one arrives at certain generalized...

Holonomic ansatz | Finite element method | Holonomic function | Inverse inequality | Zeilberger's algorithm | Symbolic determinant evaluation | 68W30 | 65N12 | 15A45 | MSC primary 33F10 | 05A20 | 65F15 | 15A15 | secondary 65N30 | MATHEMATICS, APPLIED | FINITE-ELEMENTS | COMPUTER ALGEBRA | PROOF | Analysis | Research institutes

Holonomic ansatz | Finite element method | Holonomic function | Inverse inequality | Zeilberger's algorithm | Symbolic determinant evaluation | 68W30 | 65N12 | 15A45 | MSC primary 33F10 | 05A20 | 65F15 | 15A15 | secondary 65N30 | MATHEMATICS, APPLIED | FINITE-ELEMENTS | COMPUTER ALGEBRA | PROOF | Analysis | Research institutes

Journal Article

Analysis and Geometry in Metric Spaces, ISSN 2299-3274, 12/2018, Volume 6, Issue 1, pp. 174 - 191

We consider Lipschitz maps with values in quasi-metric spaces and extend such maps to finitely many points. We prove that in this context every 1-Lipschitz map...

54C20 | 30L05 | Lipschitz extension | M-Matrix | 15A45 | Metric transforms | MATHEMATICS | MAPS | Mathematics - Metric Geometry

54C20 | 30L05 | Lipschitz extension | M-Matrix | 15A45 | Metric transforms | MATHEMATICS | MAPS | Mathematics - Metric Geometry

Journal Article

Journal of inequalities and applications, ISSN 1025-5834, 2017, Volume 2017, Issue 1, pp. 1 - 11

A new localization set for generalized eigenvalues is obtained. It is shown that the new set is tighter than that in (Numer. Linear Algebra Appl. 16: 883-898,...

generalized eigenvalue | inclusion set | matrix pencil | MATHEMATICS | MATHEMATICS, APPLIED | Eigenvalues | Localization | Linear algebra | Eigen values | 15A48 | Research | 15A45

generalized eigenvalue | inclusion set | matrix pencil | MATHEMATICS | MATHEMATICS, APPLIED | Eigenvalues | Localization | Linear algebra | Eigen values | 15A48 | Research | 15A45

Journal Article

The Rocky Mountain journal of mathematics, ISSN 0035-7596, 2014, Volume 44, Issue 1, pp. 203 - 221

This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear...

MATHEMATICS | SEMIGROUPS | SYSTEMS | UNITARY DILATIONS | MATRICES | CONTRACTIONS | 15A45 | 47A57 | 47A20

MATHEMATICS | SEMIGROUPS | SYSTEMS | UNITARY DILATIONS | MATRICES | CONTRACTIONS | 15A45 | 47A57 | 47A20

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 1/2019, Volume 113, Issue 1, pp. 255 - 266

We focus on the improvements for Young inequality. We give elementary proof for known results by Dragomir, and we give remarkable notes and some comparisons....

Young inequality and operator inequality | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Applications of Mathematics | 26D20 and 15A45 | 26D07 | MATHEMATICS | Inequalities | Mathematics - Classical Analysis and ODEs

Young inequality and operator inequality | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Applications of Mathematics | 26D20 and 15A45 | 26D07 | MATHEMATICS | Inequalities | Mathematics - Classical Analysis and ODEs

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2016, Volume 368, Issue 10, pp. 7153 - 7188

We say that a family \{\mathbold {x}_i \,\vert \, i\in [m]\} satisfies the k if \Vert\sum _{i\in I}\mathbold {x}_i\Vert\leq 1-element subsets I\subseteq...

STEINER PROBLEM | MATHEMATICS | PROOF | SPACES | BOUNDS | MATRICES

STEINER PROBLEM | MATHEMATICS | PROOF | SPACES | BOUNDS | MATRICES

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 05/2015, Volume 425, Issue 1, pp. 489 - 507

Entrywise powers of symmetric matrices preserving positivity, monotonicity or convexity with respect to the Loewner ordering arise in various applications, and...

Loewner ordering | Convexity | Entrywise powers | Monotonicity | Positivity | Rank constraints | DOUBLY NONNEGATIVE MATRICES | MATHEMATICS | MATHEMATICS, APPLIED | MATRIX SUBADDITIVITY INEQUALITY | CRITICAL EXPONENT | NORMS

Loewner ordering | Convexity | Entrywise powers | Monotonicity | Positivity | Rank constraints | DOUBLY NONNEGATIVE MATRICES | MATHEMATICS | MATHEMATICS, APPLIED | MATRIX SUBADDITIVITY INEQUALITY | CRITICAL EXPONENT | NORMS

Journal Article

16.
Full Text
Reverses of Young Type Inequalities for Matrices Using the Classical Kantorovich Constant

Results in Mathematics, ISSN 1422-6383, 3/2019, Volume 74, Issue 1, pp. 1 - 10

In this article, we give some reverses of Young type inequalities which were established by Burqan and Khandaqji (J Math Inequal 9:113–120, 2015) applying the...

reverse Young type inequality | Hilbert–Schmidt norm | 15A45 | Mathematics, general | matrix inequalities | Mathematics | classical Kantorovich constant | 15A60 | 47A30 | MATHEMATICS | MATHEMATICS, APPLIED | Hilbert-Schmidt norm | HEINZ INEQUALITIES

reverse Young type inequality | Hilbert–Schmidt norm | 15A45 | Mathematics, general | matrix inequalities | Mathematics | classical Kantorovich constant | 15A60 | 47A30 | MATHEMATICS | MATHEMATICS, APPLIED | Hilbert-Schmidt norm | HEINZ INEQUALITIES

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 2010, Volume 433, Issue 1, pp. 263 - 296

The inertia of a Hermitian matrix is defined to be a triplet composed of the numbers of the positive, negative and zero eigenvalues of the matrix counted with...

Hermitian matrix | Rank | 15A09 | Moore-Penrose inverse | 15A24 | 15A57 | Hermitian solution | 15A45 | Matrix expression | Inertia | Equality | Block matrix | Matrix equation | Inequality | NONNEGATIVE-DEFINITE | MATHEMATICS, APPLIED | INVERSES | MATHEMATICS | BICLIQUE DECOMPOSITIONS

Hermitian matrix | Rank | 15A09 | Moore-Penrose inverse | 15A24 | 15A57 | Hermitian solution | 15A45 | Matrix expression | Inertia | Equality | Block matrix | Matrix equation | Inequality | NONNEGATIVE-DEFINITE | MATHEMATICS, APPLIED | INVERSES | MATHEMATICS | BICLIQUE DECOMPOSITIONS

Journal Article

Numerical Algorithms, ISSN 1017-1398, 3/2016, Volume 71, Issue 3, pp. 613 - 630

New bounds for the infinity norm of the inverse of Nekrasov matrices, which involve a parameter, are given. And then we determine the optimal value of the...

Nekrasov matrices | Algorithms | Algebra | Infinity norm | 15A45 | Numerical Analysis | Computer Science | Numeric Computing | Theory of Computation | H-matrices | 65F35 | 15A60 | MATHEMATICS, APPLIED | Norms | Mathematical models | Inverse | Numerical analysis | Infinity | Optimization

Nekrasov matrices | Algorithms | Algebra | Infinity norm | 15A45 | Numerical Analysis | Computer Science | Numeric Computing | Theory of Computation | H-matrices | 65F35 | 15A60 | MATHEMATICS, APPLIED | Norms | Mathematical models | Inverse | Numerical analysis | Infinity | Optimization

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

Numerische Mathematik, ISSN 0029-599X, 2/2016, Volume 132, Issue 2, pp. 303 - 328

The best approximation of a matrix by a low-rank matrix can be obtained by the singular value decomposition. For large-sized matrices this approach is too...

Mathematical Methods in Physics | 65Fxx | 15A45 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 65F30 | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | Mathematics, general | Mathematics | 15A18 | MATHEMATICS, APPLIED | SINGULAR-VALUE DECOMPOSITION

Mathematical Methods in Physics | 65Fxx | 15A45 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 65F30 | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | Mathematics, general | Mathematics | 15A18 | MATHEMATICS, APPLIED | SINGULAR-VALUE DECOMPOSITION

Journal Article

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